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In the stochastic orienteering problem, we are given a finite metric space, where each node contains a job with some deterministic reward and a random processing time. The processing time distributions are known and independent across nodes. However the actual processing time of a job is not known until it is completely processed. The objective is to compute a nonanticipatory policy to visit nodes (and run the corresponding jobs) so as to maximize the total expected reward, subject to the total distance traveled plus the total processing time being at most a given budget of B. This problem combines aspects of the stochastic knapsack problem with uncertain item sizes as well as the deterministic orienteering problem. In this paper, we consider both nonadaptive and adaptive policies for Stochastic Orienteering. We present a constant-factor approximation algorithm for the nonadaptive version and an O(log logB)-approximation algorithm for the adaptive version. We extend both these results to directed metrics and a more general sequence orienteering problem. Finally, we address the stochastic orienteering problem when the node rewards are also random and possibly correlated with the processing time and obtain an O(log n logB)-approximation algorithm; here n is the number of nodes in the metric. All our results for adaptive policies also bound the corresponding "adaptivity gaps". [ABSTRACT FROM AUTHOR]

High availability communication networks with very low failure rates are often designed by using physical diversity, i.e., the traffic between a given pair of nodes is routed by using several physically disjoint paths. The selection of the pair of routes that maximizes the connectivity of a node is not an easy problem, because such connectivity cannot be expressed as an additive function of the availability of links and nodes in the path pairs. Previous algorithms for searching the optimal route use additive costs, which can be a loose assumption either when high failure rates can be locally present, or when fully disjoints paths do not exist. In this paper, we construct a Bayesian network to encode the probabilistic relation between the connectivity of a node and the availability of nodes and links. The problem of selecting an optimal pair of routes becomes equivalent to optimizing the structure of the Bayesian network. By introducing appropriate approximations on the double route availability equations, we propose a new algorithm, which outperforms other classical methods when there are sporadic high error rate elements in the network. Simulations and an application example in an electric transport telecontrol network show the performance of the method when compared to standard search. [ABSTRACT FROM AUTHOR]

An edge-bicolored graph G = ( V , R ∪ B ) is called Red/Blue-split graph if there exists a partition I B and I R of V such that I B and I R are independent sets in ( V , B ) and ( V , R ) , respectively. Red/Blue-split graphs generalize several well studied graph classes including split graphs, bipartite graphs and König–Egerváry graphs. In this paper we consider the algorithmic complexity of various optimization problems like minimum edge (or vertex) deletion and maximum edge (or vertex) induced subgraph related to Red/Blue split graphs. All these problems are NP -hard and thus we look at them from algorithmic paradigms that are meant for coping with NP -hardness. We obtain various hardness as well as algorithmic results for these problems in the realm of approximation algorithms and parameterized complexity. The main tool we use to obtain all our results is polynomial time transformations between appropriate problems. On the way, we also resolve some problems related to inapproximability about certain optimization problems mentioned by Korach et al. (2006) [17] . [ABSTRACT FROM AUTHOR]

Being the unbalanced version of the famous Min s – t Cut problem, the Min k -Size s – t Cut problem asks to find a k -size s – t cut with the minimum capacity, where a k -size s – t cut means an s – t cut with its s -side having size at most k . This problem is fundamental and has extensive applications, especially in community identification in social and information networks. It is known that the Min k -Size s – t Cut problem is NP-hard and can be approximated within O ( log ⁡ n ) , where n is the number of vertices in the input graph. In this paper, we give a new approximation algorithm for the Min k -Size s – t Cut problem based on the parametric flow technique. The algorithm is very simple and has only three lines to state. Its approximation ratio is k + 1 k + 1 − k ⁎ , where k ⁎ is the size of the s -side of an optimal solution. [ABSTRACT FROM AUTHOR]

For two positive integers m , k and a connected graph G = ( V , E ) with a nonnegative vertex weight function w , the balanced m -connected k -partition problem, denoted as BC m P k , is to find a partition of V into k disjoint nonempty vertex subsets ( V 1 , V 2 , … , V k ) such that each G [ V i ] (the subgraph of G induced by V i ) is m -connected, and min 1 ≤ i ≤ k ⁡ { w ( V i ) } is maximized. The optimal value of BC m P k on graph G is denoted as β m ⁎ ( G , k ) , that is, β m ⁎ ( G , k ) = max ⁡ min 1 ≤ i ≤ k ⁡ { w ( V i ) } , where the maximum is taken over all m -connected k -partition of G . In this paper, we study the BC 2 P k problem on interval graphs, and obtain the following results. (1) For k = 2 , a 4/3-approximation algorithm is given for BC 2 P 2 on 4-connected interval graphs. (2) In the case that there exists a vertex v with weight at least W / k , where W is the total weight of the graph, we prove that the BC 2 P k problem on a 2 k -connected interval graph G can be reduced to the BC 2 P k − 1 problem on the ( 2 k − 1 ) -connected interval graph G − v . In the case that every vertex has weight at most W / k , we prove a lower bound β 2 ⁎ ( G , k ) ≥ W / ( 2 k − 1 ) for 2 k -connected interval graph G . (3) Assuming that weight w is integral, a pseudo-polynomial time algorithm is obtained. Combining this pseudo-polynomial time algorithm with the above lower bound, a fully polynomial time approximation scheme (FPTAS) is obtained for the BC 2 P k problem on 2 k -connected interval graphs. [ABSTRACT FROM AUTHOR]

This paper presents a novel parametric representation for bidirectional texture functions. Our method mainly relies on two original techniques, namely, multivariate spherical radial basis functions (SRBFs) and optimized parameterization. First, since the surface appearance of a real-world object is frequently a mixed effect of different physical factors, the proposed sum-of-products model based on multivariate SRBFs especially provides an intrinsic and efficient representation for heterogenous materials. Second, optimized parameterization particularly aims at overcoming the major disadvantage of traditional fixed parameterization. By using a parametric model to account for variable transformations, the parameterization process can be tightly integrated with multivariate SRBFs into a unified framework. Finally, a hierarchical fitting algorithm for bidirectional texture functions is developed to exploit spatial coherence and reduce computational cost. Our experimental results further reveal that the proposed representation can easily achieve high-quality approximation and real-time rendering performance. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we deal with several reoptimization variants of the Steiner tree problem in graphs obeying a sharpened β-triangle inequality. A reoptimization algorithm exploits the knowledge of an optimal solution to a problem instance for finding good solutions for a locally modified instance. We show that, in graphs satisfying a sharpened triangle inequality (and even in graphs where edge-costs are restricted to the values 1 and for an arbitrary small ), Steiner tree reoptimization still is NP-hard for several different types of local modifications, and even APX-hard for some of them. As for the upper bounds, for some local modifications, we design linear-time -approximation algorithms, and even polynomial-time approximation schemes, whereas for metric graphs , none of these reoptimization variants is known to permit a PTAS. As a building block for some of these algorithms, we employ a 2β-approximation algorithm for the classical Steiner tree problem on such instances, which might be of independent interest since it improves over the previously best known ratio for any . [Copyright &y& Elsevier]

The scan chain insertion problem is one of the mandatory logic insertion design tasks. The scanning of designs is a very efficient way of improving their testability. But it does impact size and performance, depending on the stitching ordering of the scan chain. In this paper, we propose a graph-based approach to a stitching algorithm for automatic and optimal scan chain insertion at the RTL. Our method is divided into two main steps. The first one builds graph models for inferring logical proximity information from the design, and then the second one uses classic approximation algorithms for the traveling salesman problem to determine the best scan-stitching ordering. We show how this algorithm allows the decrease of the cost of both scan analysis and implementation, by measuring total wirelength on placed and routed benchmark designs, both academic and industrial. [ABSTRACT FROM AUTHOR]

Abstract: In generalized tree alignment problem, we are given a set of biologically related sequences and we are interested in a minimum cost evolutionary tree for . In many instances of this problem partial phylogenetic tree for is known. In such instances, we would like to make use of this knowledge to restrict the tree topologies that we consider and construct a biologically relevant minimum cost evolutionary tree. So, we propose the following natural generalization of the generalized tree alignment problem, a problem known to be MAX-SNP Hard, stated as follows: Constrained Generalized Tree Alignment Problem [S. Divakaran, Algorithms and heuristics for constrained generalized alignment problem, DIMACS Technical Report 2007-21, 2007]: Given a set of related sequences and a phylogenetic forest comprising of node-disjoint phylogenetic trees that specify the topological constraints that an evolutionary tree of needs to satisfy, construct a minimum cost evolutionary tree for . In this paper, we present constant approximation algorithms for the constrained generalized tree alignment problem. For the generalized tree alignment problem, a special case of this problem, our algorithms provide a guaranteed error bound of . [Copyright &y& Elsevier]

Abstract: Gutin et al. [G. Gutin, A. Yeo, Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number, Discrete Applied Mathematics 119 (1–2) (2002) 107–116] proved that, in the ATSP problem, a tour of weight not exceeding the weight of an average tour is of dominance ratio at least for all . (Tours with this property can be easily obtained.) In [N. Alon, G. Gutin, M. Krivelevich, Algorithms with large domination ratio, Journal on Algorithms 50 (2004) 118–131; G. Gutin, A. Vainshtein, A. Yeo, Domination analysis of combinatorial optimization problems, Discrete Applied Mathematics 129 (2–3) (2003) 513–520; G. Gutin, A. Yeo, Polynomial approximation algorithms for the TSP and the QAP with a factorial domination number, Discrete Applied Mathematics 119 (1–2) (2002) 107–116], algorithms with large dominance ratio were provided for Max Cut, Max -Sat, ATSP, and other problems. All these algorithms share a common property — they provide solutions of quality guaranteed to be not worse than the average solution value. In this paper we show that, in general, this property by itself does not necessarily ensure a good performance in terms of dominance. Specifically, we show that for the MaxSat problem, algorithms with this property might perform poorly in terms of dominance. [Copyright &y& Elsevier]

A common approach to clustering data is to view data objects as points in a metric space, and then to optimize a natural distance-based objective such as the k-median, k-means, or min-sum score. For applications such as clustering proteins by function or clustering images by subject, the implicit hope in taking this approach is that the optimal solution for the chosen objective will closely match the desired "target" clustering (e.g., a correct clustering of proteins by function or of images by who is in them). However, most distance-based objectives, including those mentioned here, are NP-hard to optimize. So, this assumption by itself is not sufficient, assuming P ≠ NP, to achieve clusterings of low-error via polynomial time algorithms. In this article, we show that we can bypass this barrier if we slightly extend this assumption to ask that for some small constant c, not only the optimal solution, but also all c-approximations to the optimal solution, differ from the target on at most some ∈ fraction of points--we call this (c, ∈)-approximation-stability. We show that under this condition, it is possible to efficiently obtain low-error clusterings even if the property holds only for values c for which the objective is known to be NP-hard to approximate. Specifically, for any constant c > 1, (c, ∈)-approximation-stability of k-median or k-means objectives can be used to efficiently produce a clustering of error O(∈) with respect to the target clustering, as can stability of the min-sum objective if the target clusters are sufficiently large. Thus, we can perform nearly as well in terms of agreement with the target clustering as if we could approximate these objectives to this NP-hard value. [ABSTRACT FROM AUTHOR]

In this article, we show that when targets are closely spaced, traditional tracking algorithms can be adjusted to perform better under a performance measure that disregards identity. More specifically, we propose an adjusted version of the joint probabilistic data association (JPDA) filter, which we call set JPDA (SJPDA). Through examples and theory we motivate the new approach, and show its possibilities. To decrease the computational requirements, we further show that the SJPDA filter can be formulated as a continuous optimization problem which is fairly easy to handle. Optimal approximations are also discussed, and an algorithm, Kullback–Leibler SJPDA (KLSJPDA), which provides optimal Gaussian approximations in the Kullback–Leibler sense is derived. Finally, we evaluate the SJPDA filter on two scenarios with closely spaced targets, and compare the performance in terms of the mean optimal subpattern assignment (MOSPA) measure with the JPDA filter, and also with the Gaussian-mixture cardinalized probability hypothesis density (GM-CPHD) filter. The results show that the SJPDA filter performs substantially better than the JPDA filter, and almost as well as the more complex GM-CPHD filter. [ABSTRACT FROM PUBLISHER]

We develop the first algorithmic approach to compute provably good ordering policies for a multiperiod, capacitated, stochastic inventory system facing stochastic nonstationary and correlated demands that evolve over time. Our approach is computationally efficient and guaranteed to produce a policy with total expected cost no more than twice that of an optimal policy. As part of our computational approach, we propose a novel scheme to account for backlogging costs in a capacitated, multiperiod environment. Our cost-accounting scheme, called the forced marginal backlogging cost-accounting scheme, is significantly different from the period-by-period accounting approach to backlogging costs used in dynamic programming; it captures the long-term impact of a decision on system performance in the presence of capacity constraints. In the likely event that the per-unit order costs are large compared to the holding and backlogging costs, a transformation of cost parameters yields a significantly improved guarantee. We also introduce new semi myopic policies based on our new cost-accounting scheme to derive bounds on the optimal base-stock levels. We show that these bounds can be used to effectively improve any policy. Finally, empirical evidence is presented that indicates that the typical performance of this approach is significantly stronger than these worst-case guarantees. [ABSTRACT FROM AUTHOR]

The local ratio technique is a methodology for the design and analysis of algorithms for a broad range of optimization problems. The technique is remarkably simple and elegant, and yet can be applied to several classical and fundamental problems (including covering problems, packing problems, and scheduling problems). The local ratio technique uses elementary math and requires combinatorial insight into the structure and properties of the problem at hand. Typically, when using the technique, one has to invent a weight function for a problem instance under which every "reasonable" solution is "good." The local ratio technique is closely related to the primal-dual schema, though it is not based on weak LP duality (which is the basis of the primal-dual approach) since it is not based on linear programming. In this survey we introduce the local ratio technique and demonstrate its use in the design and analysis of algorithms for various problems. We trace the evolution path of the technique since its inception in the 1980's, culminating with the most recent development, namely, fractional local ratio, which can be viewed as a new LP rounding technique. [ABSTRACT FROM AUTHOR]