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Deferred-acceptance auctions can be seen as heuristic algorithms to solve N P -hard allocation problems. Such auctions have been used in the context of the Incentive Auction by the US Federal Communications Commission in 2017, and they have remarkable incentive properties. Besides being strategyproof, they also prevent collusion among participants. Unfortunately, the worst-case approximation ratio of these algorithms is very low in general, but it was observed that they lead to near-optimal solutions in experiments on the specific allocation problem of the Incentive Auction. In this work, which is inspired by the telecommunications industry, we focus on a strategic version of the minimum Steiner tree problem, where the edges are owned by bidders with private costs. We design several deferred-acceptance auctions (DAAs) and compare their performance to the Vickrey–Clarke–Groves (VCG) mechanism as well as several other approximation mechanisms. We observe that, even for medium-sized inputs, the VCG mechanisms experiences impractical runtimes and that the DAAs match the approximation ratios of even the best strategy-proof mechanisms in the average case. We thus provide another example of an important practical mechanism design problem, where empirics suggest that carefully designed deferred-acceptance auctions with their superior incentive properties need not come at a cost in terms of allocative efficiency. Our experiments provide insights into the trade-off between solution quality and runtime and into the additional premium to be paid in DAAs to gain weak group-strategyproofness rather than just strategyproofness. [ABSTRACT FROM AUTHOR]

In this paper, we consider two distance-based relaxed variants of the maximum clique problem (Max Clique), named Maxd-Clique and Maxd-Club for positive integers d. Max 1-Clique and Max 1-Club cannot be efficiently approximated within a factor of n 1 - ε for any real ε > 0 unless P = NP , since they are identical to Max Clique (Håstad in Acta Math 182(1):105–142, 1999; Zuckerman in Theory Comput 3:103–128, 2007). In addition, it is NP -hard to approximate Maxd-Clique and Maxd-Club to within a factor of n 1 / 2 - ε for any fixed integer d ≥ 2 and any real ε > 0 (Asahiro et al. in Approximating maximum diameter-bounded subgraphs. In: Proc of LATIN 2010, Springer, pp 615–626, 2010; Asahiro et al. in Optimal approximation algorithms for maximum distance-bounded subgraph problems. In: Proc of COCOA, Springer, pp 586–600, 2015). As for approximability of Maxd-Clique and Maxd-Club, a polynomial-time algorithm, called ReFindStar d , that achieves an optimal approximation ratio of O (n 1 / 2) for Maxd-Clique and Maxd-Club was designed for any integer d ≥ 2 in Asahiro et al. (2015, Algorithmica 80(6):1834–1856, 2018). Moreover, a simpler algorithm, called ByFindStar d , was proposed and it was shown in Asahiro et al. (2010, 2018) that although the approximation ratio of ByFindStar d is much worse for any odd d ≥ 3 , its time complexity is better than ReFindStar d . In this paper, we implement those approximation algorithms and evaluate their quality empirically for random graphs. The experimental results show that (1) ReFindStar d can find larger d-clubs (d-cliques) than ByFindStar d for odd d, (2) the size of d-clubs (d-cliques) output by ByFindStar d is the same as ones by ReFindStar d for even d, and (3) ByFindStar d can find the same size of d-clubs (d-cliques) much faster than ReFindStar d . Furthermore, we propose and implement two new heuristics, Hclub d for Maxd-Club and Hclique d for Maxd-Clique. Then, we present the experimental evaluation of the solution size of ReFindStar d , Hclub d , Hclique d and previously known heuristic algorithms for random graphs and Erdős collaboration graphs. [ABSTRACT FROM AUTHOR]

We introduce a new technique for the analysis of online algorithms, namely bijective analysis, that is based on pair-wise comparison of the costs incurred by the algorithms. Under this framework, an algorithm A is no worse than an algorithm B if there is a bijection π defined over all request sequences of a given size such that the cost of A on σ is no more than the cost of B on B(π(σ)). We also study a relaxation of bijective analysis, termed average analysis, in which we compare two algorithms based on their corresponding average costs over request sequences of a given size. We apply these new techniques in the context of two fundamental online problems, namely paging and list update. For paging, we show that any two lazy online algorithms are equivalent under bijective analysis. This result demonstrates that, without further assumptions on characteristics of request sequences, it is unlikely, or even undesirable, to separate online paging algorithms based on their performance. However, once we restrict the set of request sequences to those exhibiting locality of reference, and in particular using a model of locality due to Albers et al. (J Comput Syst Sci 70(2):145-175, 2005), we demonstrate that Least-Recently-Used (LRU) is the unique optimal strategy according to average analysis. This is, to our knowledge, the first deterministic model to provide full theoretical backing to the empirical observation that LRU is preferable in practice. Concerning list update, we obtain similar conclusions, in terms of the bijective comparison of any two online algorithms, and in terms of the superiority (albeit not necessarily unique) of the Move-To-Front (MTF) heuristic in the presence of locality of reference. [ABSTRACT FROM AUTHOR]

We propose a method of supervised estimation with a training set of the posterior probabilities of an object belonging to classes according to a collection of known values of its features. These probabilities represent comprehensive information for solving the classification problem. They allow to solve the classification problem under various criteria (maximum probability, minimum average cost of error, etc.), which are usually chosen subjectively. Our approach to solving this problem is based on the construction of a series of approximations of special discriminant functions at whose zero points the posterior probabilities of the classes are specified during their construction. The heuristic approximation algorithm of the discriminant function used in the neighborhood of zero values is a part of the method. In the method, there is no need for additional modifications such as the Platt's calibrator for the method of support vector machines. We give model examples of applying the proposed approach and an example from medical diagnostics with real data. [ABSTRACT FROM AUTHOR]

This work proposes a unified heuristic algorithm for a large class of earliness-tardiness (E-T) scheduling problems. We consider single/parallel machine E-T problems that may or may not consider some additional features such as idle time, setup times and release dates. In addition, we also consider those problems whose objective is to minimize either the total (average) weighted completion time or the total (average) weighted flow time, which arise as particular cases when the due dates of all jobs are either set to zero or to their associated release dates, respectively. The developed local search-based metaheuristic framework is quite simple, but at the same time relies on sophisticated procedures for efficiently performing local search according to the characteristics of the problem. We present efficient move evaluation approaches for some parallel machine problems that generalize the existing ones for single machine problems. The algorithm was tested in thousands of instances of several E-T problems and particular cases. The results obtained show that our unified heuristic is capable of producing high-quality solutions when compared to the best ones available in the literature that were obtained by specific methods. Moreover, we provide an extensive annotated bibliography on the problems related to those considered in this work, where we not only indicate the approach(es) used in each publication, but we also point out the characteristics of the problem(s) considered. Beyond that, we classify the existing methods in different categories so as to have a better idea of the popularity of each type of solution procedure. [ABSTRACT FROM AUTHOR]

Approximate triple modular redundancy (ATMR) is sought for logic masking of soft errors while effectuating lower area overhead than conventional TMR through the introduction of approximate modules. However, the use of approximate modules instigates reduced fault coverage in ATMR. In this work, we target better design tradeoffs in ATMR by proposing a heuristic method that effectively utilizes a threshold for unprotected input vectors to generate good enough combinations of approximate modules for ATMR, which accomplishes higher fault coverage and reduced area overhead compared with previously proposed approaches. The key concept is to employ logic optimization techniques of prime implicant (PI) expansion and reduction for successively obtaining approximate modules such that the combination of three approximate modules appropriately functions as an ATMR. For an ATMR to function appropriately, blocking is used to ensure that at each input vector, through the prime implicant (PI) expansion and reduction technique, only one approximate module differ from the original circuit. For large circuits, clustering is utilized and comparative analysis indicates that higher fault coverage is attained through the proposed ATMR scheme while preserving the characteristic feature of reduced area overhead. With a small percentage of unprotected input vectors, we achieved substantial decrease in transistor count and greater fault detection, i.e., an improvement of up to 26.1% and 42.1%, respectively. [ABSTRACT FROM AUTHOR]

The design of a protein folding approximation algorithm is not straightforward even when a simplified model is used. The folding problem is a combinatorial problem, where approximation and heuristic algorithms are usually used to find near optimal folds of proteins primary structures. Approximation algorithms provide guarantees on the distance to the optimal solution. The folding approximation approach proposed here depends on two-dimensional cellular automata to fold proteins presented in a well-studied simplified model called the hydrophobic-hydrophilic model. Cellular automata are discrete computational models that rely on local rules to produce some overall global behavior. One-third and one-fourth approximation algorithms choose a subset of the hydrophobic amino acids to form H-H contacts. Those algorithms start with finding a point to fold the protein sequence into two sides where one side ignores H’s at even positions and the other side ignores H’s at odd positions. In addition, blocks or groups of amino acids fold the same way according to a predefined normal form. We intend to improve approximation algorithms by considering all hydrophobic amino acids and folding based on the local neighborhood instead of using normal forms. The CA does not assume a fixed folding point. The proposed approach guarantees one half approximation minus the H-H endpoints. This lower bound guaranteed applies to short sequences only. This is proved as the core and the folds of the protein will have two identical sides for all short sequences. [ABSTRACT FROM AUTHOR]

The minimum weight dominating set problem (MWDSP) is an NP-hard problem with a lot of real-world applications. Several heuristic algorithms have been presented to produce good quality solutions. However, the solution time of them grows very quickly as the size of the instance increases. In this paper, we propose a binary particle swarm optimization (FBPSO) for solving the MWDSP approximately. Based on the characteristic of MWDSP, this approach designs a new position updating rule to guide the search to a promising area. An iterated greedy tabu search is used to enhance the solution quality quickly. In addition, several stochastic strategies are employed to diversify the search and prevent premature convergence. These methods maintain a good balance between the exploration and the exploitation. Experimental studies on 106 groups of 1 060 instances show that FBPSO is able to identify near optimal solutions in a short running time. The average deviation between the solutions obtained by FBPSO and the best known solutions is 0.441%. Moreover, the average solution time of FBPSO is much less than that of other existing algorithms. In particular, with the increasing of instance size, the solution time of FBPSO grows much more slowly than that of other existing algorithms. [ABSTRACT FROM AUTHOR]

We consider the problem of scheduling a number of jobs on m identical processors sharing a continuously divisible resource. Each job j comes with a resource requirement . The job can be processed at full speed if granted its full resource requirement. If receiving only an x-portion of rj, it is processed at an x-fraction of the full speed. Our goal is to find a resource assignment that minimizes the makespan (i.e., the latest completion time). Variants of such problems, relating the resource assignment of jobs to their processing speeds, have been studied under the term discrete–continuous scheduling. Known results are either very pessimistic or heuristic in nature. In this article, we suggest and analyze a slightly simplified model. It focuses on the assignment of shared continuous resources to the processors. The job assignment to processors and the ordering of the jobs have already been fixed. It is shown that, even for unit size jobs, finding an optimal solution is NP-hard if the number of processors is part of the input. Positive results for unit size jobs include a polynomial-time algorithm for any constant number of processors. Since the running time is infeasible for practical purposes, we also provide more efficient algorithm variants: an optimal algorithm for two processors and a -approximation algorithm for m processors. [ABSTRACT FROM AUTHOR]

Home owners are typically charged differently when they consume power at different periods within a day. Specifically, they are charged more during peak periods. Thus, in this paper, we explore how scheduling algorithms can be designed to minimize the peak energy consumption of a group of homes served by the same substation. We assume that a set of demand/response switches are deployed at a group of homes to control the activities of different appliances such as air conditioners or electric water heaters in these homes. Given a set of appliances, each appliance is associated with its instantaneous power consumption and duration, our objective is to decide when to activate different appliances in order to reduce the peak power consumption. This scheduling problem is shown to be NP-Hard. To tackle this problem, we propose a set of appliance scheduling algorithms under both offline and online settings. For the offline setting, we propose a constant ratio approximation algorithm (with approximation ratio $$\frac{1+\sqrt{5}}{2}+1$$ ). For the online setting, we adopt a greedy algorithm whose competitive ratio is also bounded. We conduct extensive simulations using real-life appliance energy consumption data trace to evaluate the performance of our algorithms. Extensive evaluations show that our schedulers significantly reduce the peak demand when compared with several existing heuristics. [ABSTRACT FROM AUTHOR]

The minimum sum coloring problem (MSCP) is a variant of the well-known vertex coloring problem which has a number of AI related applications. Due to its theoretical and practical relevance, MSCP attracts increasing attention. The only existing review on the problem dates back to 2004 and mainly covers the history of MSCP and theoretical developments on specific graphs. In recent years, the field has witnessed significant progresses on approximation algorithms and practical solution algorithms. The purpose of this review is to provide a comprehensive inspection of the most recent and representative MSCP algorithms. To be informative, we identify the general framework followed by practical solution algorithms and the key ingredients that make them successful. By classifying the main search strategies and putting forward the critical elements of the reviewed methods, we wish to encourage future development of more powerful methods and motivate new applications. [ABSTRACT FROM AUTHOR]

In this paper we study the one commodity pickup-and-delivery traveling salesman problem with restricted depot (1-PDTSP-RD), which is a generalization of the classical traveling salesman problem (TSP). We first introduce a polynomial size integer programming formulation for the problem and then study the feasibility issue which is shown to be $\mathcal {NP}$ -complete by itself. In particular, we prove sufficient conditions for the feasibility of the problem and provide a polynomial algorithm to find a feasible solution. We also develop a bound on the cost of the 1-PDTSP-RD solution in terms of the cost of the TSP solution. Based on this bound, we provide a heuristic algorithm to solve the 1PDTSP-RD. Extensive numerical experiments are performed to evaluate the efficiency of both the exact and approximation algorithms. [ABSTRACT FROM AUTHOR]

Numerous applications in scheduling, such as resource allocation or steel manufacturing, can be modeled using the NP-hard Independent Set problem (given an undirected graph and an integer $$k$$ , find a set of at least $$k$$ pairwise non-adjacent vertices). Here, one encounters special graph classes like 2-union graphs (edge-wise unions of two interval graphs) and strip graphs (edge-wise unions of an interval graph and a cluster graph), on which Independent Set remains $$\mathrm{NP}$$ -hard but admits constant ratio approximations in polynomial time. We study the parameterized complexity of Independent Set on 2-union graphs and on subclasses like strip graphs. Our investigations significantly benefit from a new structural 'compactness' parameter of interval graphs and novel problem formulations using vertex-colored interval graphs. Our main contributions are as follows: [ABSTRACT FROM AUTHOR]

An uncertain version of the task scheduling problem on unrelated machines to minimize the total flow time is considered. It is assumed that processing times are not known a priori, but they belong to intervals of known bounds. The absolute regret is applied to evaluate the uncertainty, and minmax regret task scheduling problem is solved. A simple 2-approximate middle intervals time efficient algorithm is proposed. More time consuming but better in terms of the quality of solutions scatter search based heuristic algorithm is described. Its usefulness is justified via computational experiments. [ABSTRACT FROM AUTHOR]

2-Opt is probably the most basic local search heuristic for the TSP. This heuristic achieves amazingly good results on 'real world' Euclidean instances both with respect to running time and approximation ratio. There are numerous experimental studies on the performance of 2-Opt. However, the theoretical knowledge about this heuristic is still very limited. Not even its worst case running time on 2-dimensional Euclidean instances was known so far. We clarify this issue by presenting, for every $p\in\mathbb{N}$, a family of L instances on which 2-Opt can take an exponential number of steps. Previous probabilistic analyses were restricted to instances in which n points are placed uniformly at random in the unit square [0,1], where it was shown that the expected number of steps is bounded by $\tilde{O}(n^{10})$ for Euclidean instances. We consider a more advanced model of probabilistic instances in which the points can be placed independently according to general distributions on [0,1], for an arbitrary d≥2. In particular, we allow different distributions for different points. We study the expected number of local improvements in terms of the number n of points and the maximal density ϕ of the probability distributions. We show an upper bound on the expected length of any 2-Opt improvement path of $\tilde{O}(n^{4+1/3}\cdot\phi^{8/3})$. When starting with an initial tour computed by an insertion heuristic, the upper bound on the expected number of steps improves even to $\tilde{O}(n^{4+1/3-1/d}\cdot\phi^{8/3})$. If the distances are measured according to the Manhattan metric, then the expected number of steps is bounded by $\tilde{O}(n^{4-1/d}\cdot\phi)$. In addition, we prove an upper bound of $O(\sqrt[d]{\phi})$ on the expected approximation factor with respect to all L metrics. Let us remark that our probabilistic analysis covers as special cases the uniform input model with ϕ=1 and a smoothed analysis with Gaussian perturbations of standard deviation σ with ϕ∼1/ σ. [ABSTRACT FROM AUTHOR]

The partitioned EDF scheduling of implicit-deadline sporadic task systems upon identical multiprocessor platforms is considered. The problem is known to be intractable, but many different polynomial-time algorithms have been proposed for solving it approximately. These different approximation algorithms have previously been compared using utilization bounds; they are compared here using a different metric—the speedup factor. It is shown that from the perspective of their speedup factors, the best partitioning algorithms are those that (i) assign the tasks in decreasing order of utilization; and (ii) are “reasonable” in the sense that they will assign a task if there is capacity available on some processor—such algorithms include the widely-used First-Fit Decreasing, Best-Fit Decreasing, and Worst-Fit Decreasing partitioning heuristics. [ABSTRACT FROM AUTHOR]

We introduce a new framework for designing and analyzing algorithms. Our framework applies best to problems that are inapproximable according to the standard worst-case analysis. We circumvent such negative results by designing guarantees for classes of instances, parameterized according to properties of the optimal solution. Given our parameterized approximation, called PArametrized by the Signature of the Solution (PASS) approximation, we design algorithms with optimal approximation ratios for problems with additive and submodular objective functions such as the capacitated maximum facility location problems. We consider two types of algorithms for these problems. For greedy algorithms, our framework provides a justification for preferring a certain natural greedy rule over some alternative greedy rules that have been used in similar contexts. For LP-based algorithms, we show that the natural LP relaxation for these problems is not optimal in our framework. We design a new LP relaxation and show that this LP relaxation coupled with a new randomized rounding technique is optimal in our framework. In passing, we note that our results strictly improve over previous results of Kleinberg et al. (J. ACM 51(2):263-280, ) concerning the approximation ratio of the greedy algorithm. [ABSTRACT FROM AUTHOR]

We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. For the unweighted case, we prove that a local-search algorithm yields a PTAS. For the weighted case, we suggest a novel rounding scheme based on an LP relaxation of the problem, which leads to a constant-factor approximation. Most previous algorithms for maximum independent set (in geometric settings) relied on packing arguments that are not applicable in this case. As such, the analysis of both algorithms requires some new combinatorial ideas, which we believe to be of independent interest. [ABSTRACT FROM AUTHOR]

In the capacitated facility location problem with hard capacities, we are given a set of facilities, $${\mathcal{F}}$$, and a set of clients $${\mathcal{D}}$$ in a common metric space. Each facility i has a facility opening cost f and capacity u that specifies the maximum number of clients that may be assigned to this facility. We want to open some facilities from the set $${\mathcal{F}}$$ and assign each client to an open facility so that at most u clients are assigned to any open facility i. The cost of assigning client j to facility i is given by the distance c, and our goal is to minimize the sum of the facility opening costs and the client assignment costs. The only known approximation algorithms that deliver solutions within a constant factor of optimal for this NP-hard problem are based on local search techniques. It is an open problem to devise an approximation algorithm for this problem based on a linear programming lower bound (or indeed, to prove a constant integrality gap for any LP relaxation). We make progress on this question by giving a 5-approximation algorithm for the special case in which all of the facility costs are equal, by rounding the optimal solution to the standard LP relaxation. One notable aspect of our algorithm is that it relies on partitioning the input into a collection of single-demand capacitated facility location problems, approximately solving them, and then combining these solutions in a natural way. [ABSTRACT FROM AUTHOR]

Consideration was given to the multi-index problems of linear and integer linear programming of the transport type. An approach based on the study of reducibility of the multi-index transport problems to that of seeking a flow on the network was proposed. For the multi-index problems with decomposition structure, a reduction scheme enabling one to solve the original multi-index problem using the cyclic decomposition of the minimum-cost flow of the auxiliary flow problem was constructed. The developed method underlies the heuristic algorithm to solve the NP-hard integer multi-index problem with a system of constraints featuring decompositional properties and general cost matrix. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of ϵ-efficiency for vector optimization problems. This extends and unifies various notions of approximate solutions in the literature. Some properties for this new class of approximate solutions are established, and several existence results, as well as nonlinear scalarizations, are obtained by means of the Ekeland's variational principle. Moreover, under the assumption of generalized subconvex functions, we derive the linear scalarization and the Lagrange multiplier rule for approximate solutions based on the scalarization in Asplund spaces. [ABSTRACT FROM AUTHOR]

This paper presents a heuristic algorithm for solving a job-shop scheduling problem with sequence dependent setup times and min/max separation constraints among the activities (SDST-JSSP/ max). The algorithm relies on a core constraint-based search procedure, which generates consistent orderings of activities that require the same resource by incrementally imposing precedence constraints on a temporally feasible solution. Key to the effectiveness of the search procedure is a conflict sampling method biased toward selection of most critical conflicts and coupled with a non-deterministic choice heuristic to guide the base conflict resolution process. This constraint-based search is then embedded within a larger iterative-sampling search framework to broaden search space coverage and promote solution optimization. The efficacy of the overall heuristic algorithm is demonstrated empirically both on a set of previously studied job-shop scheduling benchmark problems with sequence dependent setup times and by introducing a new benchmark with setups and generalized precedence constraints. [ABSTRACT FROM AUTHOR]

We present an approximation algorithm for the problem of finding a minimum set of edges in a given graph G whose removal from G leaves a graph in which each connected component is a path. It achieves a ratio of $\frac {10}{7}$ and runs in O( n) time, where n is the number of vertices in the input graph. The previously best approximation algorithm for this problem achieves a ratio of 2 and runs in O( n) time. [ABSTRACT FROM AUTHOR]

In the pervasive e-business applications covering large geographical areas and involving many RFID readers or sensors, broker deployment strategies have a direct effect on the deployment cost and collaboration efficiency. By analyzing the deployment cost and collaboration basis, this paper proposes a model for the broker deployment problem, and presents two heuristic algorithms for the multi-object optimization of broker deployment, where one is for the deployment area which contains the zones forbidden to place brokers in, and the other is for the deployment area without any forbidden zone. Experiments are conducted to demonstrate the effectiveness of the proposed algorithms. The experimental results also show the deployment algorithms have the advantage of being low cost of deployment. Moreover, the brokers deployed carry relatively balanced loads and messages are forwarded from an event source to a broker over a small number of hops. [ABSTRACT FROM AUTHOR]

composite algorithm is developed for the classical problem of scheduling independent jobs on identical parallel machines with the objective of minimizing the makespan. The algorithm at first obtains a family of initial partial solutions and combines these partial solutions until a feasible solution is generated. Then local search procedures are used for improving the solution. The effectiveness of this approach is evaluated through extensive computational comparisons with recent improvement heuristics for different classes of benchmark instances. [ABSTRACT FROM AUTHOR]

In this paper we propose a novel message-passing algorithm, the so-called Action-GDL, as an extension to the generalized distributive law (GDL) to efficiently solve DCOPs. Action-GDL provides a unifying perspective of several dynamic programming DCOP algorithms that are based on GDL, such as DPOP and DCPOP algorithms. We empirically show how Action-GDL using a novel distributed post-processing heuristic can outperform DCPOP, and by extension DPOP, even when the latter uses the best arrangement provided by multiple state-of-the-art heuristics. [ABSTRACT FROM AUTHOR]

Given a wireless network, we want to assign each node a transmission power, which will enable transmission between any two nodes (via other nodes). Moreover, due to possible faults, we want to have at least k vertex-disjoint paths from any node to any other, where k is some fixed integer, depending on the reliability of the nodes. The goal is to achieve this directed k-strong connectivity with a minimal overall power assignment. The problem is NP-Hard for any k ≥ 1 already for planar networks. Here we first present an optimal power assignment for uniformly spaced nodes on a line for any k ≥ 1. We also prove a number of useful properties of power assignment which are also of independent interest. Based on it, we design an approximation algorithm for linear radio networks with factor $$\hbox{min}\left\{2,\left(\frac {\Updelta} {\delta}\right)^\alpha \right\},$$ where Δ and δ are the maximal and minimal distances between adjacent nodes respectively and parameter α ≥ 1 being the distance-power gradient. We then extend it to the weighted version. Finally, we develop an approximation algorithm with factor O( k2), for planar case, which is, to the best of our knowledge, the first non-trivial result for this problem. [ABSTRACT FROM AUTHOR]

Frequent itemset mining over data streams becomes a hot topic in data mining and knowledge discovery in recent years, and has been applied to different areas. However, the setting of a minimum support threshold needs some domain knowledge. It will bring a lot of difficulties or much burden to users if the support threshold is not set reasonably. It is interesting for users to find top- K frequent itemsets over data streams. In this paper, a dynamical incremental approximate algorithm TOPSIL-Miner is presented to mine top- K significant itemsets in landmark windows. A new data structure, TOPSIL-Tree, is designed to store the potential significant itemsets and other data structures of maximum support list, ordered item list, TOPSET and minimum support list are devised to maintain information about mining results. Moreover, three optimal strategies are exploited to reduce time and space cost of the algorithm: (1) pruning trivial nodes in the current data stream, (2) promoting mining support threshold during mining process adaptively and heuristically, and (3) promoting pruning threshold dynamically. The accuracy of the algorithm is also analyzed. Extensive experiments are performed to evaluate the good effectiveness and the high efficiency and precision of the algorithm. [ABSTRACT FROM AUTHOR]

We consider an agent seeking to obtain an item, potentially available at different locations in a physical environment. The traveling costs between locations are known in advance, but there is only probabilistic knowledge regarding the possible prices of the item at any given location. Given such a setting, the problem is to find a plan that maximizes the probability of acquiring the good while minimizing both travel and purchase costs. Sample applications include agents in search-and-rescue or exploration missions, e.g., a rover on Mars seeking to mine a specific mineral. These probabilistic physical search problems have been previously studied, but we present the first approximation and heuristic algorithms for solving such problems on general graphs. We establish an interesting connection between these problems and classical graph-search problems, which led us to provide the approximation algorithms and hardness of approximation results for our settings. We further suggest several heuristics for practical use, and demonstrate their effectiveness with simulation on a real graph structure. [ABSTRACT FROM AUTHOR]