Solving the winner determination problem via a weighted maximum clique heuristic

Wu, Qinghua; Hao, Jin‐Kao

doi:10.1016/j.eswa.2014.07.027

Cited by 39 publications

(36 citation statements)

References 24 publications

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“…Moreover, MWCLQ is even more efficient than some state-of-the-art heuristic algorithms on some relatively hard instances. For example, MWCLQ solves in108 in 101.04 seconds, while the heuristic algorithm (Wu & Hao, 2015), based on tabu search takes, 113.53 seconds to find the solution with probability 0.73. Ignoring the difference of running environments, MWCLQ is faster than the tabu search algorithm on in108.…”

Section: Application Of Mwclq For the Winner Determination Problemmentioning

confidence: 99%

“…We also selected MaxHS using the direct encoding, which is the most effective MaxSAT solver to solve an MWC instance, in this comparison. We used the benchmark provided by Lau and Goh (2002), which has been widely used as benchmark purpose to test WDP algorithms (Guo, Lim, Rodrigues, & Zhu, 2006;Sghir, Hao, Jaafar, & Ghédira, 2014;Wu & Hao, 2015). Instances in this benchmark are generated by incorporating the following factors, i.e., a pricing factor which models a bidder's acceptable price range for each bid, a preference factor which takes into account bidder's preferences among bids, and a fairness factor which measures the fairness in distributing items among bidders.…”

Section: Application Of Mwclq For the Winner Determination Problemmentioning

confidence: 99%

“…In our experiment, we transformed WDP to MWC first and then formulated it with integer programming. Another method is used by Wu and Hao (2015) to formulate WDP directly into integer programming. The method appears to be slightly more effective than the transformation in our experiment, but it does not affect our comparison, because the only instances CPLEX is able to solve within 3600 seconds are also from REL-1000-500 with this transformation.…”

Section: Application Of Mwclq For the Winner Determination Problemmentioning

confidence: 99%

“…It is computationally equivalent to problems like the weighted set packing problem. The MWC problem appears in a variety of realworld applications, such as protein structure predictions (Mascia, Cilia, Brunato, & Passerini, 2010), coding theory (Zhian, Sabaei, Javan, & Tavallaie, 2013), combinatorial auctions (Wu & Hao, 2015), computer vision (Ma & Latecki, 2012;Zhang, Javed, & Shah, 2014a), etc. For example, in the video object segmentation problem, a challenging task is to select a region having high objectness score and sharing similar appearance, which can be solved by an MWC algorithm (Ma & Latecki, 2012).…”

Section: Introductionmentioning

confidence: 99%

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An Exact Algorithm Based on MaxSAT Reasoning for the Maximum Weight Clique Problem

Fang¹,

Li²,

Xu³

2016

jair

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Recently, MaxSAT reasoning is shown very effective in computing a tight upper bound for a Maximum Clique (MC) of a (unweighted) graph. In this paper, we apply MaxSAT reasoning to compute a tight upper bound for a Maximum Weight Clique (MWC) of a wighted graph. We first study three usual encodings of MWC into weighted partial MaxSAT dealing with hard clauses, which must be satisfied in all solutions, and soft clauses, which are weighted and can be falsified. The drawbacks of these encodings motivate us to propose an encoding of MWC into a special weighted partial MaxSAT formalism, called LW (Literal-Weighted) encoding and dedicated for upper bounding an MWC, in which both soft clauses and literals in soft clauses are weighted. An optimal solution of the LW MaxSAT instance gives an upper bound for an MWC, instead of an optimal solution for MWC. We then introduce two notions called the Top-k literal failed clause and the Top-k empty clause to extend classical MaxSAT reasoning techniques, as well as two sound transformation rules to transform an LW MaxSAT instance. Successive transformations of an LW MaxSAT instance driven by MaxSAT reasoning give a tight upper bound for the encoded MWC. The approach is implemented in a branch-and-bound algorithm called MWCLQ. Experimental evaluations on the broadly used DIMACS benchmark, BHOSLIB benchmark, random graphs and the benchmark from the winner determination problem show that our approach allows MWCLQ to reduce the search space significantly and to solve MWC instances effectively. Consequently, MWCLQ outperforms state-of-the-art exact algorithms on the vast majority of instances. Moreover, it is surprisingly effective in solving hard and dense instances.

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Section: Application Of Mwclq For the Winner Determination Problemmentioning

confidence: 99%

Section: Application Of Mwclq For the Winner Determination Problemmentioning

confidence: 99%

Section: Application Of Mwclq For the Winner Determination Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Exact Algorithm Based on MaxSAT Reasoning for the Maximum Weight Clique Problem

Fang¹,

Li²,

Xu³

2016

jair

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“…Consequently, a maximum weight clique corresponds to an optimal allocation. WDP instances, available via cspLib [44] and originally created by Lau and Goh [33], have been used as a benchmark suite by Fang et al [22] and Wu and Hao [64] for comparing one maximum weight clique algorithm against another. But what do these instances look like?…”

Section: The Winner Determination Problemmentioning

confidence: 99%

On Maximum Weight Clique Algorithms, and How They Are Evaluated

McCreesh

Prosser

Simpson

et al. 2017

Lecture Notes in Computer Science

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Abstract. Maximum weight clique and maximum weight independent set solvers are often benchmarked using maximum clique problem instances, with weights allocated to vertices by taking the vertex number mod 200 plus 1. For constraint programming approaches, this rule has clear implications, favouring weight-based rather than degree-based heuristics. We show that similar implications hold for dedicated algorithms, and that additionally, weight distributions affect whether certain inference rules are cost-effective. We look at other families of benchmark instances for the maximum weight clique problem, coming from winner determination problems, graph colouring, and error-correcting codes, and introduce two new families of instances, based upon kidney exchange and the Research Excellence Framework. In each case the weights carry much more interesting structure, and do not in any way resemble the 200 rule. We make these instances available in the hopes of improving the quality of future experiments.

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