72 results on '"Dachuan Xu"'
Search Results
2. Two approximation algorithms for maximizing nonnegative weakly monotonic set functions
- Author
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Min Cui, Donglei Du, Dachuan Xu, and Ruiqi Yang
- Subjects
Control and Optimization ,Computational Theory and Mathematics ,Applied Mathematics ,Discrete Mathematics and Combinatorics ,Computer Science Applications - Published
- 2023
3. Bicriteria streaming algorithms to balance gain and cost with cardinality constraint
- Author
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Yijing Wang, Donglei Du, Yanjun Jiang, and Dachuan Xu
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Mathematical optimization ,Control and Optimization ,Computer science ,Applied Mathematics ,Function (mathematics) ,Linear function ,Computer Science Applications ,Submodular set function ,Constraint (information theory) ,Cardinality ,Monotone polygon ,Computational Theory and Mathematics ,Theory of computation ,Discrete Mathematics and Combinatorics ,Computer Science::Data Structures and Algorithms ,Streaming algorithm - Abstract
Team formation plays an essential role in the labor market. In this paper, we propose two bicriteria algorithms to construct a balance between gain and cost in a team formation problem under the streaming model, subject to a cardinality constraint. We formulate the problem as maximizing the difference of a non-negative normalized monotone submodular function and a non-negative linear function. As an extension, we also consider the case where the first function is $$\gamma $$ -weakly submodular. Combining the greedy technique with the threshold method, we present bicriteria streaming algorithms and give detailed analysis for both of these models. Our analysis is competitive with that in Ene’s work.
- Published
- 2021
4. Approximation algorithms for the lower bounded correlation clustering problem
- Author
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Sai Ji, Yinhong Dong, Donglei Du, Dongzhao Wang, and Dachuan Xu
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Control and Optimization ,Computational Theory and Mathematics ,Applied Mathematics ,Discrete Mathematics and Combinatorics ,Computer Science Applications - Published
- 2022
5. A Stackelberg order execution game
- Author
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Yinhong Dong, Donglei Du, Qiaoming Han, Jianfeng Ren, and Dachuan Xu
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General Decision Sciences ,Management Science and Operations Research - Published
- 2022
6. Selfish bin packing under Harmonic mean cost sharing mechanism
- Author
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Ling Gai, Dachuan Xu, Chenchen Wu, and Weiwei Zhang
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Computer Science::Computer Science and Game Theory ,Mathematical optimization ,Control and Optimization ,Bin packing problem ,Harmonic mean ,TheoryofComputation_GENERAL ,Computational intelligence ,Upper and lower bounds ,Bin ,symbols.namesake ,Nash equilibrium ,Value (economics) ,symbols ,Price of anarchy ,Mathematics - Abstract
In this paper, we introduce the selfish bin packing problem under a new version of cost sharing mechanism based on harmonic mean. The items (as agents) are selfish and intelligent to minimize the cost they have to pay, by selecting a proper bin to fit in. The tricky part is that the one with bigger size pays less and vice versa. We present the motivations and prove the existence of pure Nash Equilibrium under this new defined cost sharing mechanism. Then we study the Price of Anarchy, which is the ratio between the objective value of worst Nash Equilibrium and that of the optimum in the case with central decision maker. We prove the upper bound to be approximately 1.722 and show a 5/3 lower bound for this problem. We then include punishment into the model and prove that in this new model, the Price of Anarchy could be decreased to 3/2.
- Published
- 2021
7. Maximization problems of balancing submodular relevance and supermodular diversity
- Author
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Xiaoyan Zhang, Dachuan Xu, Zhicheng Liu, Longkun Guo, and Donglei Du
- Subjects
Control and Optimization ,Applied Mathematics ,Approximation algorithm ,Field (mathematics) ,Function (mathematics) ,Management Science and Operations Research ,Matroid ,Computer Science Applications ,Submodular set function ,Combinatorics ,Monotone polygon ,Uniform matroid ,Supermodular function ,Mathematics - Abstract
Relevance and diversity are two desirable properties in data retrieval applications, an important field in data science and machine learning. In this paper, we consider three maximization problems to balance these two factors. The objective function in each problem is the sum of a monotone submodular function f and a supermodular function g, where f and g capture the relevance and diversity of any feasible solution, respectively. In the first problem, we consider a special supermodular diversity function g of a sum-sum format satisfying the relaxed triangle inequality, for which we propose a greedy-type approximation algorithm with an $$\left( 1-1/e,1/(2\alpha )\right) $$ -bifactor approximation ratio, improving the previous $$\left( 1/(2\alpha ),1/(2\alpha )\right) $$ -bifactor approximation ratio. In the second problem, we consider an arbitrary supermodular diversity function g, for which we propose a distorted greedy method to give a $$\min \left\{ 1-k_{f}e^{-1},1-k^{g}e^{-(1-k^{g})}\right\} $$ -approximation algorithm, improving the previous $$k_f^{-1}\left( 1-e^{-k_f(1-k^{g})}\right) $$ -approximation ratio, where $$k_f$$ and $$k^g$$ are the curvatures of the submodular function f and the supermodular funciton g, respectively. In the third problem, we generalize the uniform matroid constraint to the p matroid constraints, for which we present a local search algorithm to improve the previous $$\frac{1-k^g}{(1-k^g)k^f+p}$$ -approximation ratio to $$\min \left\{ \frac{p+1-k_f}{p(p+1)},\left( \frac{1-k^g}{p}+\frac{k^g(1-k^g)^2}{p+(1-k^g)^2}\right) \right\} $$ .
- Published
- 2021
8. Improved local search algorithms for Bregman k-means and its variants
- Author
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Dan Wu, Longkun Guo, Xiaoyun Tian, and Dachuan Xu
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021103 operations research ,Control and Optimization ,business.industry ,Applied Mathematics ,0211 other engineering and technologies ,Center (category theory) ,k-means clustering ,Piecewise constant approximation ,0102 computer and information sciences ,02 engineering and technology ,Bregman divergence ,01 natural sciences ,Computer Science Applications ,Computational Theory and Mathematics ,Computer Science::Computational Engineering, Finance, and Science ,010201 computation theory & mathematics ,Discrete Mathematics and Combinatorics ,Local search (optimization) ,business ,Algorithm ,Mathematics - Abstract
In this paper, we consider the Bregman k-means problem (BKM) which is a variant of the classical k-means problem. For an n-point set $${\mathcal {S}}$$ and $$k \le n$$ with respect to $$\mu $$ -similar Bregman divergence, the BKM problem aims first to find a center subset $$C \subseteq {\mathcal {S}}$$ with $$ \mid C \mid = k$$ and then separate $${\mathcal {S}}$$ into k clusters according to C, such that the sum of $$\mu $$ -similar Bregman divergence from each point in $${\mathcal {S}}$$ to its nearest center is minimized. We propose a $$\mu $$ -similar BregMeans++ algorithm by employing the local search scheme, and prove that the algorithm deserves a constant approximation guarantee. Moreover, we extend our algorithm to solve a variant of BKM called noisy $$\mu $$ -similar Bregman k-means++ (noisy $$\mu $$ -BKM++) which is BKM in the noisy scenario. For the same instance and purpose as BKM, we consider the case of sampling a point with an imprecise probability by a factor between $$1-\varepsilon _1$$ and $$1+ \varepsilon _2$$ for $$\varepsilon _1 \in [0,1)$$ and $$\varepsilon _2 \ge 0$$ , and obtain an approximation ratio of $$O(\log ^2 k)$$ in expectation.
- Published
- 2021
9. Approximation algorithms for the individually fair k-center with outliers
- Author
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Lu Han, Dachuan Xu, Yicheng Xu, and Ping Yang
- Subjects
Control and Optimization ,Applied Mathematics ,Business, Management and Accounting (miscellaneous) ,Management Science and Operations Research ,Computer Science Applications - Published
- 2022
10. The spherical k-means++ algorithm via local search scheme
- Author
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Xiaoyun Tian, Ling Gai, Donglei Du, and Dachuan Xu
- Subjects
021103 operations research ,Control and Optimization ,business.industry ,Applied Mathematics ,0211 other engineering and technologies ,k-means clustering ,Center (category theory) ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Measure (mathematics) ,Computer Science Applications ,Combinatorics ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Theory of computation ,Discrete Mathematics and Combinatorics ,Trigonometric functions ,Local search (optimization) ,Point (geometry) ,business ,Cluster analysis ,Mathematics - Abstract
The spherical k-means problem (SKMP) is an important variant of the k-means clustering problem (KMP). In this paper, we consider the SKMP, which aims to divide the n points in a given data point set $${\mathcal {S}}$$ into k clusters so as to minimize the total sum of the cosine dissimilarity measure from each data point to their respective closest cluster center. Our main contribution is to design an expected constant approximation algorithm for the SKMP by integrating the seeding algorithm for the KMP and the local search technique. By utilizing the structure of the clusters, we further obtain an improved LocalSearch++ algorithm involving $$\varepsilon k$$ local search steps.
- Published
- 2021
11. An approximation algorithm for the k-level facility location problem with outliers
- Author
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Lu Han, Chenchen Wu, Dandan Liu, and Dachuan Xu
- Subjects
Discrete mathematics ,021103 operations research ,Control and Optimization ,Computer science ,Total cost ,0211 other engineering and technologies ,Approximation algorithm ,010103 numerical & computational mathematics ,02 engineering and technology ,Extension (predicate logic) ,01 natural sciences ,Facility location problem ,Set (abstract data type) ,Cardinality ,Outlier ,Business, Management and Accounting (miscellaneous) ,0101 mathematics ,Integer (computer science) - Abstract
In this paper, we study the k-level facility location problem with outliers (k-LFLPWO), which is an extension of the well-known k-level facility location problem (k-LFLP). In the k-LFLPWO, we are given k facility location sets, a client location set of cardinality n and a non-negative integer $$q
- Published
- 2021
12. Regularized two-stage submodular maximization under streaming
- Author
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Ruiqi Yang, Dachuan Xu, Longkun Guo, and Dongmei Zhang
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General Computer Science - Published
- 2022
13. Sequence submodular maximization meets streaming
- Author
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Ruiqi Yang, Dachuan Xu, Longkun Guo, and Dongmei Zhang
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Control and Optimization ,Computational Theory and Mathematics ,Applied Mathematics ,Discrete Mathematics and Combinatorics ,Computer Science Applications - Published
- 2020
14. Approximating the $$\tau $$-relaxed soft capacitated facility location problem
- Author
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Yicheng Xu, Lu Han, Dongmei Zhang, and Dachuan Xu
- Subjects
021103 operations research ,Control and Optimization ,Triangle inequality ,Applied Mathematics ,0211 other engineering and technologies ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Facility location problem ,Computer Science Applications ,Metric k-center ,Combinatorics ,Set (abstract data type) ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Theory of computation ,Metric (mathematics) ,Physics::Accelerator Physics ,Discrete Mathematics and Combinatorics ,Connection (algebraic framework) ,Mathematics - Abstract
In this paper, we consider the $$\tau $$ -relaxed soft capacitated facility location problem ( $$\tau $$ -relaxed SCFLP), which extends several well-known facility location problems like the squared metric soft capacitated facility location problem (SMSCFLP), soft capacitated facility location problem (SCFLP), squared metric facility location problem and uncapacitated facility location problem. In the $$\tau $$ -relaxed SCFLP, we are given a facility set $$\mathcal {F}$$ , a client set and a parameter $$\tau \ge 1$$ . Every facility $$i \in \mathcal {F}$$ has a capacity $$u_i$$ and an opening cost $$f_i$$ , and can be opened multiple times. If facility i is opened l times, this facility can be connected by at most $$l u_i$$ clients and incurs an opening cost of $$l f_i$$ . Every facility-client pair has a connection cost. Under the assumption that the connection costs are non-negative, symmetric and satisfy the $$\tau $$ -relaxed triangle inequality, we wish to open some facilities (once or multiple times) and connect every client to an opened facility without violating the capacity constraint so as to minimize the total opening costs as well as connection costs. As our main contribution, we propose a primal-dual based $$(3 \tau + 1)$$ -approximation algorithm for the $$\tau $$ -relaxed SCFLP. Furthermore, our algorithm not only extends the applicability of the primal-dual technique but also improves the previous approximation guarantee for the SMSCFLP from $$11.18+ \varepsilon $$ to 10.
- Published
- 2020
15. Maximizing a monotone non-submodular function under a knapsack constraint
- Author
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Yishui Wang, Zhenning Zhang, Dachuan Xu, Bin Liu, and Dongmei Zhang
- Subjects
021103 operations research ,Control and Optimization ,Optimization problem ,Applied Mathematics ,0211 other engineering and technologies ,TheoryofComputation_GENERAL ,0102 computer and information sciences ,02 engineering and technology ,Maximization ,Function (mathematics) ,01 natural sciences ,Computer Science Applications ,Submodular set function ,Combinatorics ,Monotone polygon ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Theory of computation ,Discrete Mathematics and Combinatorics ,Combinatorial optimization ,Computer Science::Data Structures and Algorithms ,Greedy algorithm ,Mathematics - Abstract
Submodular optimization has been well studied in combinatorial optimization. However, there are few works considering about non-submodular optimization problems which also have many applications, such as experimental design, some optimization problems in social networks, etc. In this paper, we consider the maximization of non-submodular function under a knapsack constraint, and explore the performance of the greedy algorithm, which is characterized by the submodularity ratio $$\beta $$ and curvature $$\alpha $$ . In particular, we prove that the greedy algorithm enjoys a tight approximation guarantee of $$ (1-e^{-\alpha \beta })/{\alpha }$$ for the above problem. To our knowledge, it is the first tight constant factor for this problem. We further utilize illustrative examples to demonstrate the performance of our algorithm.
- Published
- 2020
16. Approximation algorithms for two variants of correlation clustering problem
- Author
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Dachuan Xu, Min Li, Sai Ji, and Yishui Wang
- Subjects
021103 operations research ,Control and Optimization ,Theoretical computer science ,Computer science ,Applied Mathematics ,Correlation clustering ,0211 other engineering and technologies ,Piecewise constant approximation ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,Link (geometry) ,01 natural sciences ,Telecommunications network ,Computer Science Applications ,ComputingMethodologies_PATTERNRECOGNITION ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Theory of computation ,Cluster (physics) ,Discrete Mathematics and Combinatorics ,Cluster analysis - Abstract
Correlation clustering problem is a clustering problem which has many applications such as protein interaction networks, cross-lingual link detection, communication networks, and social computing. In this paper, we introduce two variants of correlation clustering problem: correlation clustering problem on uncertain graphs and correlation clustering problem with non-uniform hard constrained cluster sizes. Both problems overcome part of the limitations of the existing variants of correlation clustering problem and have practical applications in the real world. We provide a constant approximation algorithm and two approximation algorithms for the former and the latter problem, respectively.
- Published
- 2020
17. A constant FPT approximation algorithm for hard-capacitated k-means
- Author
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Yicheng Xu, Yong Zhang, Rolf H. Möhring, Dachuan Xu, and Yifei Zou
- Subjects
021103 operations research ,Control and Optimization ,Mechanical Engineering ,0211 other engineering and technologies ,k-means clustering ,Aerospace Engineering ,Approximation algorithm ,Piecewise constant approximation ,02 engineering and technology ,Disjoint sets ,Performance guarantee ,Combinatorics ,Combinatorial optimization ,Meta heuristic ,Partition (number theory) ,021108 energy ,Electrical and Electronic Engineering ,Software ,Civil and Structural Engineering ,Mathematics - Abstract
Hard-capacitated k-means (HCKM) is one of the fundamental problems remaining open in combinatorial optimization and engineering. In HCKM, one is required to partition a given n-point set into k disjoint clusters with known capacity so as to minimize the sum of within-cluster variances. It is known to be at least APX-hard, and most of the work on it has been done from a meta heuristic or bi-criteria approximation perspective. To the best our knowledge, no constant approximation algorithm or existence proof of such an algorithm is known. As our main contribution, we propose an FPT(k) approximation algorithm with constant performance guarantee for HCKM in this paper.
- Published
- 2020
18. The seeding algorithm for spherical k-means clustering with penalties
- Author
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Min Li, Dongmei Zhang, Longkun Guo, Dachuan Xu, and Sai Ji
- Subjects
Surface (mathematics) ,021103 operations research ,Control and Optimization ,Applied Mathematics ,0211 other engineering and technologies ,k-means clustering ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Computer Science Applications ,Separable space ,Data set ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Theory of computation ,Discrete Mathematics and Combinatorics ,Trigonometric functions ,Partition (number theory) ,Cluster analysis ,Algorithm ,Mathematics - Abstract
Spherical k-means clustering as a known NP-hard variant of the k-means problem has broad applications in data mining. In contrast to k-means, it aims to partition a collection of given data distributed on a spherical surface into k sets so as to minimize the within-cluster sum of cosine dissimilarity. In the paper, we introduce spherical k-means clustering with penalties and give a $$2\max \{2,M\}(1+M)(\ln k+2)$$-approximation algorithm. Moreover, we prove that when against spherical k-means clustering with penalties but on separable instances, our algorithm is with an approximation ratio $$2\max \{3,M+1\}$$ with high probability, where M is the ratio of the maximal and the minimal penalty cost of the given data set.
- Published
- 2020
19. An approximation algorithm for the uniform capacitated k-means problem
- Author
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Donglei Du, Lu Han, Dachuan Xu, and Dongmei Zhang
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021103 operations research ,Control and Optimization ,Applied Mathematics ,0211 other engineering and technologies ,Center (category theory) ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Upper and lower bounds ,Square (algebra) ,Computer Science Applications ,Combinatorics ,Cardinality ,Computational Theory and Mathematics ,Integer ,010201 computation theory & mathematics ,Discrete Mathematics and Combinatorics ,Point (geometry) ,Local search (constraint satisfaction) ,Mathematics - Abstract
In this paper, we consider the uniform capacitated k-means problem (UC-k-means), an extension of the classical k-means problem (k-means) in machine learning. In the UC-k-means, we are given a set $$\mathcal {D}$$ of n points in d-dimensional space and an integer k. Every point in the d-dimensional space has an uniform capacity which is an upper bound on the number of points in $$\mathcal {D}$$ that can be connected to this point. Every two-point pair in the space has an associated connecting cost, which is equal to the square of the distance between these two points. We want to find at most k points in the space as centers and connect every point in $$\mathcal {D}$$ to some center without violating the capacity constraint, such that the total connecting costs is minimized. Based on the technique of local search, we present a bi-criteria approximation algorithm, which has a constant approximation guarantee and violates the cardinality constraint within a constant factor, for the UC-k-means.
- Published
- 2020
20. Non-submodular maximization on massive data streams
- Author
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Yishui Wang, Dongmei Zhang, Dachuan Xu, and Yi-Jing Wang
- Subjects
Mathematical optimization ,021103 operations research ,Control and Optimization ,Data stream mining ,Applied Mathematics ,0211 other engineering and technologies ,Context (language use) ,02 engineering and technology ,Management Science and Operations Research ,Computer Science Applications ,Submodular set function ,Constraint (information theory) ,Cardinality ,Monotone polygon ,Set function ,Business, Management and Accounting (miscellaneous) ,Streaming algorithm ,Mathematics - Abstract
The problem of maximizing a normalized monotone non-submodular set function subject to a cardinality constraint arises in the context of extracting information from massive streaming data. In this paper, we present four streaming algorithms for this problem by utilizing the concept of diminishing-return ratio. We analyze these algorithms to obtain the corresponding approximation ratios, which generalize the previous results for the submodular case. The numerical experiments show that our algorithms have better solution quality and competitive running time when compared to an existing algorithm.
- Published
- 2019
21. A Note on Submodularity Preserved Involving the Rank Functions
- Author
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Min Li, Dachuan Xu, Donglei Du, and Zhenning Zhang
- Subjects
021103 operations research ,Concave function ,0211 other engineering and technologies ,010103 numerical & computational mathematics ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Matroid ,Submodular set function ,Combinatorics ,Intersection ,Rank (graph theory) ,0101 mathematics ,Mathematics - Abstract
In many kinds of games with economic significance, it is very important to study the submodularity of functions. In this paper, we mainly study the problem of maximizing a concave function over an intersection of two matroids. We obtain that the submodularity may not be preserved, but it involves one maximal submodular problem (or minimal supermodular problem) with some conditions. Moreover, we also present examples showing that these conditions can be satisfied.
- Published
- 2019
22. Streaming algorithm for maximizing a monotone non-submodular function under d-knapsack constraint
- Author
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Dachuan Xu, Yong Zhang, Yanjun Jiang, Ruiqi Yang, and Yishui Wang
- Subjects
Mathematical optimization ,021103 operations research ,Control and Optimization ,Computer science ,0211 other engineering and technologies ,Approximation algorithm ,010103 numerical & computational mathematics ,02 engineering and technology ,Maximization ,01 natural sciences ,Submodular set function ,Constraint (information theory) ,Monotone polygon ,Cover (topology) ,Set function ,0101 mathematics ,Streaming algorithm - Abstract
Maximizing constrained submodular functions lies at the core of substantial machine learning and data mining. Specially, the case that the data come in a streaming fashion receives more attention in recent decades. In this work, we study the approximation algorithm for maximizing a non-decreasing set function under d-knapsack constraint. Based on the diminishing-return ratio for set functions, a non-trivial algorithm is devised for maximizing the set function without submodularity. Our results cover some known results and provide an effective method for the maximization on set functions no matter they are submodular or not. We also run the algorithm to handle the application of support selection for sparse linear regression. Numerical results show that the output quality of the algorithm is good.
- Published
- 2019
23. Minimizing Ratio of Monotone Non-submodular Functions
- Author
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Yanjun Jiang, Dongmei Zhang, Yi-Jing Wang, and Dachuan Xu
- Subjects
Discrete mathematics ,021103 operations research ,0211 other engineering and technologies ,Inverse ,010103 numerical & computational mathematics ,02 engineering and technology ,Management Science and Operations Research ,Curvature ,01 natural sciences ,Performance guarantee ,Submodular set function ,Monotone polygon ,Set function ,0101 mathematics ,Mathematics - Abstract
In this paper, we investigate the problem of minimizing the ratio of normalized non-negative monotone non-submodular set function f and normalized non-negative monotone set function g. We take advantage of the greedy technique and get a performance guarantee depending on the generalized curvature and inverse generalized curvature of f, as well as the submodularity ratio of g. Our results generalize the works of Bai et al. (Algorithms for optimizing the ratio of submodular functions. In: Proceedings of the 33rd International Conference on Machine Learning, 2016) and Qian et al. (Optimizing ratio of monotone set functions. In: Proceedings of the 26th International Joint Conference on Artificial Intelligence, 2017).
- Published
- 2019
24. Approximation algorithm for squared metric two-stage stochastic facility location problem
- Author
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Yishui Wang, Dachuan Xu, Jin Zhang, Min Li, and Chenchen Wu
- Subjects
Mathematical optimization ,021103 operations research ,Control and Optimization ,Computer science ,Applied Mathematics ,0211 other engineering and technologies ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Facility location problem ,Computer Science Applications ,Connection (mathematics) ,Set (abstract data type) ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Metric (mathematics) ,Theory of computation ,Discrete Mathematics and Combinatorics ,Stage (hydrology) ,Integer programming - Abstract
In this paper, we consider a variant of the classical uncapacitated facility location problem, so-called squared metric two-stage stochastic facility location problem (SM-2-SFLP) which can treat the uncertainty of the set of clients and facility costs. We assume that the connection cost is squared metric, a variant of the metric case which is widely researched. We give a new 0–1 integer linear programming for SM-2-SFLP. Based on the new formulation, we apply two known algorithms to SM-2-SFLP, and analyze the approximation ratio and per-scenario bound respectively.
- Published
- 2019
25. Convergence and correctness of belief propagation for the Chinese postman problem
- Author
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Xiaoyan Zhang, Fengwei Li, Dachuan Xu, Guowei Dai, and Yuefang Sun
- Subjects
021103 operations research ,Control and Optimization ,Correctness ,Optimization problem ,Applied Mathematics ,0211 other engineering and technologies ,02 engineering and technology ,Directed graph ,Management Science and Operations Research ,Belief propagation ,Computer Science Applications ,Linear programming relaxation ,Route inspection problem ,Graph (abstract data type) ,Graphical model ,Algorithm ,Mathematics - Abstract
Belief Propagation (BP), a distributed, message-passing algorithm, has been widely used in different disciplines including information theory, artificial intelligence, statistics and optimization problems in graphical models such as Bayesian networks and Markov random fields. Despite BP algorithm has a great success in many application fields and many progress about BP algorithm has been made, the rigorous analysis about the correctness and convergence of BP algorithm are known in only a few cases for arbitrary graph. In this paper, we will investigate the correctness and convergence of BP algorithm for determining the optimal solutions of the Chinese postman problem in both undirected and directed graphs. As a main result, we prove that BP algorithm converges to the optimal solution of the undirected Chinese postman problem within O(n) iterations where n represents the number of vertices, provided that the optimal solution is unique. For the directed case, we consider the directed Chinese postman problem with capacity and show that BP algorithm also converges to its optimal solution after O(n) iterations, as long as its corresponding linear programming relaxation has the unique optimal solution.
- Published
- 2019
26. Local search approximation algorithms for the sum of squares facility location problems
- Author
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Dongmei Zhang, Peng Zhang, Dachuan Xu, Zhenning Zhang, and Yishui Wang
- Subjects
Discrete mathematics ,021103 operations research ,Control and Optimization ,business.industry ,Applied Mathematics ,Dimension (graph theory) ,0211 other engineering and technologies ,Explained sum of squares ,Center (category theory) ,Approximation algorithm ,02 engineering and technology ,Management Science and Operations Research ,Facility location problem ,Computer Science Applications ,Set (abstract data type) ,Computer Science::Logic in Computer Science ,Business, Management and Accounting (miscellaneous) ,Local search (optimization) ,business ,Cluster analysis ,Mathematics - Abstract
In this paper, we study the sum of squares facility location problem (SOS-FLP) which is an important variant of k-means clustering. In the SOS-FLP, we are given a client set $$ \mathcal {C} \subset \mathbb {R}^p$$ and a uniform center opening cost $$f>0$$ . The goal is to open a finite center subset $$F \subset \mathbb {R}^p$$ and to connect each client to the closest open center such that the total cost including center opening cost and the sum of squares of distances is minimized. The SOS-FLP is introduced firstly by Bandyapadhyay and Varadarajan (in: Proceedings of SoCG 2016, Article No. 14, pp 14:1–14:15, 2016) which present a PTAS for the fixed dimension case. Using local search and scaling techniques, we offer the first constant approximation algorithm for the SOS-FLP with general dimension. We further consider the discrete version of SOS-FLP, in which we are given a finite candidate center set with nonuniform opening cost comparing with the aforementioned (continue) SOS-FLP. By exploring the structures of local and optimal solutions, we claim that the approximation ratios are $$7.7721+ \epsilon $$ and $$9+ \epsilon $$ for the continue and discrete SOS-FLP respectively.
- Published
- 2019
27. A spectral partitioning algorithm for maximum directed cut problem
- Author
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Dongmei Zhang, Donglei Du, Zhenning Zhang, Chenchen Wu, and Dachuan Xu
- Subjects
021103 operations research ,Control and Optimization ,Applied Mathematics ,Rounding ,0211 other engineering and technologies ,0102 computer and information sciences ,02 engineering and technology ,Directed graph ,01 natural sciences ,Computer Science Applications ,Arc (geometry) ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Theory of computation ,Discrete Mathematics and Combinatorics ,Quadratic programming ,Algorithm ,MathematicsofComputing_DISCRETEMATHEMATICS ,Mathematics - Abstract
We investigate the maximum directed cut (MaxDC) problem by designing a spectral partitioning algorithm. Given a directed graph with nonnegative arc weights, we wish to obtain a bipartition of the vertices such that the total weight of the directed cut arcs is maximized. Relaxing the MaxDC problem as a quadratic program allows us to explore combinatorial properties of the optimal solution, leading to a 0.272-approximation algorithm via the technique of spectral partitioning rounding.
- Published
- 2019
28. A general method of active friending in different diffusion models in social networks
- Author
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Hua Wang, Chuangen Gao, Dachuan Xu, Ruiqi Yang, Weili Wu, and Shuyang Gu
- Subjects
Mathematical optimization ,021103 operations research ,Computational complexity theory ,Computer science ,Communication ,Node (networking) ,0211 other engineering and technologies ,0102 computer and information sciences ,02 engineering and technology ,Maximization ,01 natural sciences ,Computer Science Applications ,Submodular set function ,Human-Computer Interaction ,Set (abstract data type) ,Cardinality ,010201 computation theory & mathematics ,Knapsack problem ,Media Technology ,Combinatorial optimization ,Information Systems - Abstract
Active friending is a problem in social networks that is to assist a user to build a relationship to a target user by sending invitations to a set of intermediate users; the goal is to maximize the acceptance probability at the target node taking advantage of the social influence through the network formed by the intermediate nodes. In this paper, we convert the original formulated active friending problem of nonsubmodular maximization subject to cardinality constraint into a submodular cost submodular knapsack problem in the IC model, and we show that the two problems are equivalent. We similarly make the conversion on the active friending in the LT model. Then we give a general combinatorial optimization algorithm to solve active friending problems in both the IC model and the LT model with a guaranteed approximation. We analyze the computational complexity of the problem and the algorithm performance. The effectiveness of the generalized method is verified on real data sets.
- Published
- 2020
29. Local search approximation algorithms for the k-means problem with penalties
- Author
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Zhenning Zhang, Chenchen Wu, Chunlin Hao, Dachuan Xu, and Dongmei Zhang
- Subjects
021103 operations research ,Control and Optimization ,Generalization ,Applied Mathematics ,0211 other engineering and technologies ,Center (category theory) ,Explained sum of squares ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Computer Science Applications ,Combinatorics ,Computational Theory and Mathematics ,Integer ,010201 computation theory & mathematics ,Theory of computation ,Discrete Mathematics and Combinatorics ,Backslash ,Local search (constraint satisfaction) ,Mathematics - Abstract
In this paper, we study the k-means problem with (nonuniform) penalties (k-MPWP) which is a natural generalization of the classic k-means problem. In the k-MPWP, we are given an n-client set $$ {\mathcal {D}} \subset {\mathbb {R}}^d$$ , a penalty cost $$p_j>0$$ for each $$j \in {\mathcal {D}}$$ , and an integer $$k \le n$$ . The goal is to open a center subset $$F \subset {\mathbb {R}}^d$$ with $$ |F| \le k$$ and to choose a client subset $$P \subseteq {\mathcal {D}} $$ as the penalized client set such that the total cost (including the sum of squares of distance for each client in $$ {\mathcal {D}} \backslash P $$ to the nearest open center and the sum of penalty cost for each client in P) is minimized. We offer a local search $$( 81+ \varepsilon )$$ -approximation algorithm for the k-MPWP by using single-swap operation. We further improve the above approximation ratio to $$( 25+ \varepsilon )$$ by using multi-swap operation.
- Published
- 2018
30. A local search approximation algorithm for a squared metric k-facility location problem
- Author
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Zhenning Zhang, Dongmei Zhang, Peng Zhang, Yishui Wang, and Dachuan Xu
- Subjects
Discrete mathematics ,021103 operations research ,Control and Optimization ,business.industry ,Applied Mathematics ,0211 other engineering and technologies ,Explained sum of squares ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Facility location problem ,Computer Science Applications ,Metric k-center ,Metric space ,Computational Theory and Mathematics ,Integer ,010201 computation theory & mathematics ,Metric (mathematics) ,Physics::Accelerator Physics ,Discrete Mathematics and Combinatorics ,Local search (optimization) ,business ,Mathematics - Abstract
In this paper, we introduce a squared metric k-facility location problem (SM-k-FLP) which is a generalization of the squared metric facility location problem and k-facility location problem (k-FLP). In the SM-k-FLP, we are given a client set $$\mathcal {C}$$ and a facility set $$\mathcal {F} $$ from a metric space, a facility opening cost $$f_i \ge 0$$ for each $$ i \in \mathcal {F}$$ , and an integer k. The goal is to open a facility subset $$F \subseteq \mathcal {F}$$ with $$ |F| \le k$$ and to connect each client to the nearest open facility such that the total cost (including facility opening cost and the sum of squares of distances) is minimized. Using local search and scaling techniques, we offer a constant approximation algorithm for the SM-k-FLP.
- Published
- 2018
31. Approximation algorithms for the robust facility leasing problem
- Author
-
Min Li, Lu Han, Dachuan Xu, and Dongmei Zhang
- Subjects
Discrete mathematics ,Control and Optimization ,Total cost ,Computer science ,Approximation algorithm ,ComputerApplications_COMPUTERSINOTHERSYSTEMS ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Facility location problem ,Set (abstract data type) ,Cardinality ,010201 computation theory & mathematics ,0202 electrical engineering, electronic engineering, information engineering ,020201 artificial intelligence & image processing ,Open interval ,Integer (computer science) - Abstract
In this paper, we consider the robust facility leasing problem (RFLE), which is a variant of the well-known facility leasing problem. In this problem, we are given a facility location set, a client location set of cardinality n, time periods $$\{1, 2, \ldots , T\}$$ and a nonnegative integer $$q < n$$ . At each time period t, a subset of clients $$D_{t}$$ arrives. There are K lease types for all facilities. Leasing a facility i of a type k at any time period s incurs a leasing cost $$f_i^{k}$$ such that facility i is opened at time period s with a lease length $$l_k$$ . Each client in $$D_t$$ can only be assigned to a facility whose open interval contains t. Assigning a client j to a facility i incurs a serving cost $$c_{ij}$$ . We want to lease some facilities to serve at least $$n-q$$ clients such that the total cost including leasing and serving cost is minimized. Using the standard primal–dual technique, we present a 6-approximation algorithm for the RFLE. We further offer a refined 3-approximation algorithm by modifying the phase of constructing an integer primal feasible solution with a careful recognition on the leasing facilities.
- Published
- 2018
32. Solving the degree-concentrated fault-tolerant spanning subgraph problem by DC programming
- Author
-
Ding-Zhu Du, Panos M. Pardalos, Dachuan Xu, Zaixin Lu, Yishui Wang, Zhao Zhang, and Chenchen Wu
- Subjects
Mathematical optimization ,021103 operations research ,Spanning subgraph ,Degree (graph theory) ,General Mathematics ,Numerical analysis ,0211 other engineering and technologies ,Dc programming ,Fault tolerance ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,010201 computation theory & mathematics ,Relaxation (approximation) ,Numerical tests ,Convex function ,Software ,Mathematics - Abstract
In this paper, we consider the maximum and minimum versions of degree-concentrated fault-tolerant spanning subgraph problem which has many applications in network communications. We prove that both this two problems are NP-hard. For the maximum version, we use DC programming relaxation to propose a heuristic algorithm. Numerical tests indicate that the proposed algorithm is efficient and effective. For the minimum version, we also formulate it as a DC program, and show that the DC algorithm does not perform well for this problem.
- Published
- 2018
33. Approximate efficiency and strategy-proofness for moneyless mechanisms on single-dipped policy domain
- Author
-
Qiaoming Han, Yicheng Xu, Donglei Du, and Dachuan Xu
- Subjects
Mechanism design ,Mathematical optimization ,Control and Optimization ,Applied Mathematics ,media_common.quotation_subject ,05 social sciences ,Approximation algorithm ,02 engineering and technology ,Interval (mathematics) ,Management Science and Operations Research ,Facility location problem ,Computer Science Applications ,Domain (software engineering) ,Voting ,0502 economics and business ,0202 electrical engineering, electronic engineering, information engineering ,Business, Management and Accounting (miscellaneous) ,050206 economic theory ,020201 artificial intelligence & image processing ,Point (geometry) ,Mathematical economics ,Algorithmic mechanism design ,media_common ,Mathematics - Abstract
The single-dipped domain can be used to model any allocation problem where a single output must be chosen in an interval with the assumption that agents’ preferences have a single most loathful point (the dip) in the interval, and the preferences are increasing as one moves away from that dip. Practical domains like this appear in political voting system where each voter has his most-hated candidate and alternative candidates are evaluated by their proximity to this candidate or in obnoxious location problem, where each agent prefers to have the obnoxious location to be distant from his own location, among others. We first characterize deterministic and anonymous strategy-proof and group strategy-proof mechanisms on single-dipped public policy domain, complementing the well-known results on single-peaked policy domain first investigated by Moulin (Pub. Choice 35:437–455, 1980). Then we consider the tradeoff between strategy-proofness and efficiency by applying our characterization. As concrete applications of our results, we extend existing models and results, and resolve several open questions related to the obnoxious facility location game from the algorithmic mechanism design literature.
- Published
- 2017
34. Preface
- Author
-
Bo Chen, Dachuan Xu, and Guochuan Zhang
- Subjects
Mathematical optimization ,Control and Optimization ,Computational Theory and Mathematics ,Computer science ,Applied Mathematics ,Discrete Mathematics and Combinatorics ,Combinatorial optimization ,Computer Science Applications - Published
- 2021
35. An approximation algorithm for soft capacitated k-facility location problem
- Author
-
Chenchen Wu, Dachuan Xu, Yanjun Jiang, Dongmei Zhang, and Donglei Du
- Subjects
Control and Optimization ,Applied Mathematics ,Structure (category theory) ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,Condensed Matter::Mesoscopic Systems and Quantum Hall Effect ,01 natural sciences ,Facility location problem ,Computer Science Applications ,Combinatorics ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Theory of computation ,Hardware_INTEGRATEDCIRCUITS ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,020201 artificial intelligence & image processing ,Mathematics - Abstract
We present a $$(20+{5}/{n})$$(20+5/n)-approximation algorithm for the non-uniform soft capacitated k-facility location problem, violating the capacitated constrains by no more than a factor of 25. The main technique is based on the primal---dual algorithm for the soft capacitated facility location problem, and the exploitation of the combinatorial structure of the fractional solution for the soft capacitated k-facility location problem.
- Published
- 2017
36. A local search approximation algorithm for the uniform capacitated k-facility location problem
- Author
-
Donglei Du, Dongmei Zhang, Dachuan Xu, and Lu Han
- Subjects
Mathematical optimization ,021103 operations research ,Control and Optimization ,Computer science ,Applied Mathematics ,0211 other engineering and technologies ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Facility location problem ,Computer Science Applications ,Set (abstract data type) ,Constraint (information theory) ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,1-center problem ,Theory of computation ,Discrete Mathematics and Combinatorics ,Cardinality (SQL statements) ,Local search (constraint satisfaction) - Abstract
In the uniform capacitated k-facility location problem (UC-k-FLP), we are given a set of facilities and a set of clients. Every client has a demand. Every facility have an opening cost and an uniform capacity. For each client–facility pair, there is an unit service cost to serve the client with unit demand by the facility. The total demands served by a facility cannot exceed the uniform capacity. We want to open at most k facilities to serve all the demands of the clients without violating the capacity constraint such that the total opening and serving cost is minimized. The main contribution of this work is to present the first combinatorial bi-criteria approximation algorithm for the UC-k-FLP by violating the cardinality constraint.
- Published
- 2017
37. Approximation algorithms for the robust/soft-capacitated 2-level facility location problems
- Author
-
Dachuan Xu, Dongmei Zhang, Peng Zhang, and Chenchen Wu
- Subjects
Mathematical optimization ,021103 operations research ,Control and Optimization ,Applied Mathematics ,0211 other engineering and technologies ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Facility location problem ,Computer Science Applications ,Primal dual ,010201 computation theory & mathematics ,Business, Management and Accounting (miscellaneous) ,Connection (algebraic framework) ,Mathematics - Abstract
In this work, we consider the robust/soft-capacitated 2-level facility location problems. For the robust version, we propose a primal-dual based $$(3+\epsilon )$$ -approximation algorithm via construction of an adapted instance which explores some open facilities in the optimal solution. For the soft-capacitated version, we propose a $$ (4+ 1/ (e-1) +\epsilon )$$ -approximation algorithm via construction of the associated uncapacitated version whose connection cost is re-defined appropriately.
- Published
- 2017
38. An approximation algorithm for the dynamic facility location problem with outliers
- Author
-
Dongmei Zhang, Donglei Du, Dachuan Xu, and Yanjun Jiang
- Subjects
Mathematical optimization ,021103 operations research ,Control and Optimization ,Linear programming ,0211 other engineering and technologies ,Approximation algorithm ,Computational intelligence ,010103 numerical & computational mathematics ,02 engineering and technology ,01 natural sciences ,Minimax approximation algorithm ,Facility location problem ,Outlier ,1-center problem ,0101 mathematics ,Integer (computer science) ,Mathematics - Abstract
In this article, we investigate the dynamic (multi-period) facility location problem with potentially unserved clients or outliers. We propose a 3-approximation primal-dual algorithm based on an integer linear program formulation of the problem. We further improve the approximation ratio to 2 by combining the cost scaling and greedy improvement techniques.
- Published
- 2017
39. A Primal-Dual Algorithm for the Generalized Prize-Collecting Steiner Forest Problem
- Author
-
Dachuan Xu, Lu Han, Chenchen Wu, and Donglei Du
- Subjects
Vertex (graph theory) ,Connected component ,Discrete mathematics ,Primal dual algorithm ,021103 operations research ,0211 other engineering and technologies ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,Management Science and Operations Research ,01 natural sciences ,Primal dual ,Combinatorics ,010201 computation theory & mathematics ,Steiner forest ,Connectivity ,Mathematics - Abstract
In this paper, we consider the generalized prize-collecting Steiner forest problem, extending the prize-collecting Steiner forest problem. In this problem, we are given a connected graph $$G = (V, E)$$ and a set of vertex sets $${\mathcal {V}} = \{V_1, V_2,\cdots , V_{l}\}$$ . Every edge in E has a nonnegative cost, and every vertex set in $${\mathcal {V}}$$ has a nonnegative penalty cost. For a given edge set $$F\subseteq E$$ , vertex set $$V_i\in {\mathcal {V}}$$ is said to be connected by edge set F if $$V_i$$ is in a connected component of the F-spanned subgraph. The objective is to find such an edge set F such that the total edge cost in F and the penalty cost of the vertex sets not connected by F is minimized. Our main contribution is to give a 3-approximation algorithm for this problem via the primal-dual method.
- Published
- 2017
40. A 5-approximation algorithm for the k-prize-collecting Steiner tree problem
- Author
-
Dachuan Xu, Chenchen Wu, Lu Han, and Donglei Du
- Subjects
Discrete mathematics ,Control and Optimization ,Spanning tree ,Shortest-path tree ,010102 general mathematics ,Prim's algorithm ,0102 computer and information sciences ,Minimum spanning tree ,k-minimum spanning tree ,01 natural sciences ,Steiner tree problem ,Combinatorics ,symbols.namesake ,010201 computation theory & mathematics ,TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY ,symbols ,Gomory–Hu tree ,0101 mathematics ,MathematicsofComputing_DISCRETEMATHEMATICS ,Mathematics ,Minimum degree spanning tree - Abstract
In this paper, we consider the k-prize-collecting Steiner tree problem (k-PCST), extending both the prize-collecting Steiner tree problem (PCST) and the k-minimum spanning tree problem (k-MST). In this problem, we are given a connected graph \(G = (V, E)\), a root vertex r and an integer k. Every edge in E has a nonnegative cost. Every vertex in V has a nonnegative penalty cost. We want to find an r-rooted tree F that spans at least k vertices such that the total cost, including the edge cost of the tree F and the penalty cost of the vertices not spanned by F, is minimized. Our main contribution is to present a 5-approximation algorithm for the k-PCST via the methods of primal–dual and Lagrangean relaxation.
- Published
- 2017
41. A sparse enhanced indexation model with chance and cardinality constraints
- Author
-
Yu-Hong Dai, Dachuan Xu, Meihua Wang, and Fengmin Xu
- Subjects
Semidefinite programming ,Mathematical optimization ,021103 operations research ,Control and Optimization ,Applied Mathematics ,0211 other engineering and technologies ,02 engineering and technology ,Management Science and Operations Research ,Stock market index ,Computer Science Applications ,Cardinality ,0202 electrical engineering, electronic engineering, information engineering ,Capital asset pricing model ,Probability distribution ,Portfolio ,020201 artificial intelligence & image processing ,Random variable ,Indexation ,Mathematics - Abstract
Enhanced indexation aims to construct a portfolio to track and outperform the performance of a stock market index by employing both passive and active fund management strategies. This paper presents a novel sparse enhanced indexation model with chance and cardinality constraints. Its goal is to maximize the excess return that can be attained with a high probability, while the model allows a fund manger to limit the number of stocks in the portfolio and specify the maximum tolerable relative market risk. In particular, we model the asset returns as random variables and estimate their probability distributions by the Capital Asset Pricing Model or Fama-French 3-factor model, and measure the relative market risk with the coherent semideviation risk function. We deal with the chance constraint via distributionally robust approach and present a second-order cone programming and a semidefinite programming safe approximation for the model under different sets of potential distribution functions. A hybrid genetic algorithm is applied to solve the NP-hard problem. Numerical tests are conducted on the real data sets from major international stock markets, including USA, UK, Germany and China. The results demonstrate that the proposed model and the method can efficiently solve the enhanced indexation problem and our approach can generally achieve sparse tracking portfolios with good out-of-sample excess returns and high robustness.
- Published
- 2017
42. An approximation algorithm for k-facility location problem with linear penalties using local search scheme
- Author
-
Yishui Wang, Dachuan Xu, Chenchen Wu, and Donglei Du
- Subjects
Control and Optimization ,business.industry ,Applied Mathematics ,Contrast (statistics) ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,Extension (predicate logic) ,01 natural sciences ,Facility location problem ,Computer Science Applications ,Combinatorics ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Scheme (mathematics) ,Theory of computation ,0202 electrical engineering, electronic engineering, information engineering ,Discrete Mathematics and Combinatorics ,020201 artificial intelligence & image processing ,Local search (optimization) ,business ,Mathematics - Abstract
In this paper, we consider an extension of the classical facility location problem, namely k-facility location problem with linear penalties. In contrast to the classical facility location problem, this problem opens no more than k facilities and pays a penalty cost for any non-served client. We present a local search algorithm for this problem with a similar but more technical analysis due to the extra penalty cost, compared to that in Zhang (Theoretical Computer Science 384:126–135, 2007). We show that the approximation ratio of the local search algorithm is $$2 + 1/p + \sqrt{3+ 2/p+ 1/p^2} + \epsilon $$ , where $$p \in {\mathbb {Z}}_+$$ is a parameter of the algorithm and $$\epsilon >0$$ is a positive number.
- Published
- 2016
43. Approximation algorithms for precedence-constrained identical machine scheduling with rejection
- Author
-
Xianzhao Zhang, Dachuan Xu, Donglei Du, and Chenchen Wu
- Subjects
Mathematical optimization ,Machine scheduling ,021103 operations research ,Control and Optimization ,Job shop scheduling ,Linear programming ,Computer science ,Applied Mathematics ,Rounding ,0211 other engineering and technologies ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Computer Science Applications ,Scheduling (computing) ,Submodular set function ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Theory of computation ,Discrete Mathematics and Combinatorics - Abstract
We study a precedence-constrained identical parallel machine scheduling problem with rejection. There is a communication delay between any two jobs connected in the precedence network where jobs may be rejected with penalty. The goal is to minimize the sum of the makespan and the rejection cost. We propose two 3-approximation algorithms for this problem under linear and submodular rejection costs respectively. These two algorithms are both based on linear programming rounding technique.
- Published
- 2016
44. An approximation algorithm for the nth power metric facility location problem with linear penalties
- Author
-
Chenchen Wu, Yishui Wang, Donglei Du, and Dachuan Xu
- Subjects
Control and Optimization ,Approximation algorithm ,020207 software engineering ,0102 computer and information sciences ,02 engineering and technology ,01 natural sciences ,Upper and lower bounds ,Facility location problem ,Power (physics) ,Metric k-center ,Combinatorics ,010201 computation theory & mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Connection (algebraic framework) ,Mathematics - Abstract
We consider the nth power metric facility location problem with linear penalties (M $$^n$$ FLPLP) in this work, extending both the nth power metric facility location problem (M $$^n$$ FLP) and the metric facility location problem with linear penalties (MFLPLP). We present an LP-rounding based approximation algorithm to the M $$^n$$ FLPLP with bi-factor approximation ratio $$(\gamma _f, \gamma _c)$$ , where $$\gamma _f$$ and $$\gamma _c$$ are the ratios corresponding to facility, and connection and penalty costs respectively. Finally we show that the bi-factor curve is close to the lower bound $$(\gamma _f, 1 + (3^n - 1) e^{-\gamma _f})$$ when the facility factor $$\gamma _f > 2$$ for the M $$^2$$ FLPLP.
- Published
- 2015
45. Local search algorithm for universal facility location problem with linear penalties
- Author
-
Dachuan Xu, Yicheng Xu, Donglei Du, and Chenchen Wu
- Subjects
Service (business) ,Mathematical optimization ,Control and Optimization ,business.industry ,Applied Mathematics ,Approximation algorithm ,020207 software engineering ,0102 computer and information sciences ,02 engineering and technology ,Function (mathematics) ,Management Science and Operations Research ,01 natural sciences ,Facility location problem ,Computer Science Applications ,Set (abstract data type) ,010201 computation theory & mathematics ,1-center problem ,0202 electrical engineering, electronic engineering, information engineering ,Local search (optimization) ,business ,Mathematics - Abstract
The universal facility location problem generalizes several classical facility location problems, such as the uncapacitated facility location problem and the capacitated location problem (both hard and soft capacities). In the universal facility location problem, we are given a set of demand points and a set of facilities. We wish to assign the demands to facilities such that the total service as well as facility cost is minimized. The service cost is proportional to the distance that each unit of the demand has to travel to its assigned facility. The open cost of facility i depends on the amount z of demand assigned to i and is given by a cost function $$f_i(z)$$fi(z). In this work, we extend the universal facility location problem to include linear penalties, where we pay certain penalty cost whenever we refuse serving some demand points. As our main contribution, we present a ($$7.88+\epsilon $$7.88+∈)-approximation local search algorithm for this problem.
- Published
- 2015
46. Treatment of the distal fracture in radioulna based on the volar wrist dual channel approach and postoperative X-ray diagnosis
- Author
-
Jinhao Zeng, Yinwei Bai, Shaoxiao Yu, Zhenwei Zhang, Huixin Lin, Xuelang Ye, Zheng Li, and Dachuan Xu
- Subjects
Adult ,Male ,medicine.medical_specialty ,Biomedical Engineering ,Biophysics ,General Physics and Astronomy ,Wrist ,Fracture Fixation, Internal ,Young Adult ,medicine ,Humans ,Radiology, Nuclear Medicine and imaging ,Carpal tunnel ,Postoperative Period ,Lead (electronics) ,business.industry ,Pronator quadratus muscle ,Middle Aged ,Ulna Fractures ,Median nerve ,Surgery ,Radiography ,body regions ,medicine.anatomical_structure ,Fracture (geology) ,Female ,Distal radius fracture ,Radius Fractures ,business - Abstract
The fracture of the distal ulna and radius is a kind of fracture that results in high morbidity and occurrence rate and contributes to about one-sixth of the entire body’s fracture. In this study, we implemented the improved palmar wrist surgery by a volar wrist dual channel approach. Between 2011 and 2014, we have treated 67 distal radius fracture patients. We divided them into two parts randomly, and treat them by the Carpometacarpal direct approach solution and dual wrist palmar surgical approach solution respectively. After the surgery, the differences in the incidence of median nerve irritation are significant (P
- Published
- 2015
47. An approximation algorithm for the balanced Max-3-Uncut problem using complex semidefinite programming rounding
- Author
-
Dachuan Xu, Donglei Du, Wenqing Xu, and Chenchen Wu
- Subjects
Semidefinite embedding ,Semidefinite programming ,Mathematical optimization ,021103 operations research ,Control and Optimization ,Linear programming ,Applied Mathematics ,Rounding ,0211 other engineering and technologies ,Graph partition ,Approximation algorithm ,0102 computer and information sciences ,02 engineering and technology ,Function (mathematics) ,01 natural sciences ,Computer Science Applications ,Computational Theory and Mathematics ,010201 computation theory & mathematics ,Discrete Mathematics and Combinatorics ,Combinatorial optimization ,Mathematics - Abstract
Graph partition problems have been investigated extensively in combinatorial optimization. In this work, we consider an important graph partition problem which has applications in the design of VLSI circuits, namely, the balanced Max-3-Uncut problem. We formulate the problem as a discrete linear program with complex variables and propose an approximation algorithm with an approximation ratio of 0.3456 using a semidefinite programming rounding technique along with a greedy swapping step afterwards to guarantee the balanced constraint. Our analysis utilizes a bivariate function, rather than the univariate function in previous work.
- Published
- 2015
48. Anatomical study for flexor hallucis longus tendon transfer in treatment of Achilles tendinopathy
- Author
-
Keith L. Wapner, Weigang Yin, Haijiao Mao, Dachuan Xu, Wenwei Dong, and Zengyuan Shi
- Subjects
Adult ,Male ,medicine.medical_specialty ,animal structures ,Adolescent ,medicine.medical_treatment ,Tendon Transfer ,Achilles Tendon ,Pathology and Forensic Medicine ,Tendons ,Asian People ,Tendon transfer ,Cadaver ,medicine ,Humans ,Radiology, Nuclear Medicine and imaging ,Aged ,Aged, 80 and over ,Achilles tendon ,Foot ,business.industry ,musculoskeletal, neural, and ocular physiology ,Anatomy ,Middle Aged ,musculoskeletal system ,medicine.disease ,body regions ,medicine.anatomical_structure ,Flexor hallucis longus ,Tendinopathy ,Orthopedic surgery ,Flexor Digitorum Longus ,Female ,Surgery ,Anatomic Landmarks ,business ,tissues ,Posterior Tibial Tendon Dysfunction - Abstract
The purpose of the study was to describe the anatomical variations of the connection between the flexor hallucis longus (FHL) and flexor digitorum longus (FDL) tendons in the knot of Henry in Asians, and quantify the length of FHL tendon graft with different incisions.Sixty-four embalmed feet of 32 cadavers were analyzed anatomically with respect to the individual cross-links in the planta pedis. Single incision technique graft length was measured from the musculotendinous junction of FHL and the point at sustentaculum tali. Double incision technique was measured from musculotendinous junction of FHL and the level of the master knot of Henry. Additionally, minimally invasive incision technique was measured from musculotendinous junction of FHL to the first interphalangeal joint. These three techniques were then combined to determine the total potential tendon graft length obtainable using different approach.Only two different configurations were found. Type 1, a tendinous slip branched from the FHL to the FDL (62 of 64 feet). Type 2, a slip branched from the FHL to the FDL and another slip from the FDL to FHL (2 of 64). The average length of the FHL graft available from a single incision measured 5.08 cm (range 3.32-10.35, SD = 1.09), double incision technique measured 6.72 cm (range 4.69-12.09, SD = 1.03), and minimally invasive incision measured 17.49 cm (range 13.51-20.52, SD = 1.80). The difference between the lengths obtained from these three techniques was statistically significant (p0.001).The absence of no attachment and FDL tendon to the FHL between the two tendons in the foot may be more frequent than previously reported. Only two configurations of the anatomical relationship were found in this study. In over 96 % of the feet, a proximal to distal connection from the FHL to the FDL was found, which might contribute to the residual function of the lesser toes after FDL transfer.
- Published
- 2014
49. Approximation algorithms for the priority facility location problem with penalties
- Author
-
Fengmin Wang, Dachuan Xu, and Chenchen Wu
- Subjects
Mathematical optimization ,Augmentation procedure ,1-center problem ,Computer Science (miscellaneous) ,Complex system ,Approximation algorithm ,Facility location problem ,Information Systems ,Mathematics ,Primal dual - Abstract
This paper considers the priority facility location problem with penalties. The authors develop a primal-dual 3-approximation algorithm for this problem. Combining with the greedy augmentation procedure, the authors further improve the previous ratio 3 to 1.8526.
- Published
- 2014
50. An improved per-scenario bound for the two-stage stochastic facility location problem
- Author
-
Dachuan Xu, Donglei Du, and Chenchen Wu
- Subjects
Mathematical optimization ,General Mathematics ,1-center problem ,Approximation algorithm ,Stage (hydrology) ,Facility location problem ,Mathematics - Abstract
We study the two-stage stochastic facility location problem (2-SFLP) by proposing an LP (location problem)-rounding approximation algorithm with 2.3613 per-scenario bound for this problem, improving the previously best per-scenario bound of 2.4957.
- Published
- 2014
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