A Stochastic Local Search Approach to Vertex Cover

In topological mapping, perceptual aliasing can cause different places to appear indistinguishable to the robot. In case of severely corrupted or non-available odometry information, topological mapping is difficult as the robot is challenged with the loop-closing problem; that is to determine whether it has visited a particular place before.In this article we propose to use neighbourhood information to disambiguate otherwise indistinguishable places. Using neighbourhood information for place disambiguation is an approach that neither depends on a specific choice of sensors nor requires geometric information such as odometry. Local neighbourhood information is extracted from a sequence of observations of visited places.In experiments using either sonar or visual observations from an indoor environment the benefits of using neighbourhood clues for the disambiguation of otherwise identical vertices are demonstrated. Over 90% of the maps we obtain are isomorphic with the ground truth. The choice of the robot's sensors does not impact the results of the experiments much.

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“…Richter et al 2007). SLS algorithms have been successfully applied to NP-complete problems such as satisfiability and constraint satisfaction.…”

Section: Map Induction Using a Stochastic Local Searchmentioning

confidence: 93%

Topological map induction using neighbourhood information of places

2012

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“…According to the reported results, the overall performance of these heuristics are not competitive compared with recent local search methods. Finally, it is worthwhile to mention that some recent edge weighting local search approaches for the equivalent minimum vertex cover problem, such as COVER (Richter, Helmert, & Gretton, 2007) and EWCC (Cai, Su, & Sattar, 2011), report very good results on the DIMACS and BHOSLIB benchmarks.…”

Section: Accepted Manuscriptmentioning

confidence: 98%

A review on algorithms for maximum clique problems

Hao

2015

European Journal of Operational Research

262

168

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The maximum clique problem (MCP) is to determine in a graph a clique (i.e., a complete subgraph) of maximum cardinality. The MCP is notable for its capability of modeling other combinatorial problems and real-world applications. As one of the most studied NP-hard problems, many algorithms are available in the literature and new methods are continually being proposed. Given that the two existing surveys on the MCP date back to 1994 and 1999 respectively, one primary goal of this paper is to provide an updated and comprehensive review on both exact and heuristic MCP algorithms, with a special focus on recent developments. To be informative, we identify the general framework followed by these algorithms and pinpoint the key ingredients that make them successful. By classifying the main search strategies and putting forward the critical elements of the most relevant clique methods, this review intends to encourage future development of more powerful methods and motivate new applications of the clique approaches.

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“…Since we deal with the MIS problem, we use the complements of the original graphs. For instances with no known optimum, we report the best results available at the time of writing (as listed in Grosso et al 2008;Richter et al 2007). …”

Section: Instancesmentioning

confidence: 99%

“…The SAT family contains transformed satisfiability instances originally from the SAT'04 competition, available at Xu (2004) and tested in Grosso et al (2008), Richter et al (2007). All optima are known.…”

Section: Instancesmentioning

confidence: 99%

“…Most successful heuristics (Battiti and Protasi 2001;Grosso et al 2004Grosso et al , 2008Hansen et al 2004;Katayama et al 2005;Pullan and Hoos 2006;Richter et al 2007) maintain a single current solution that is steadily modified by very simple operations, such as individual insertions, individual deletions, and swaps (replacing a vertex by one of its neighbors). In particular, many algorithms use the notion of plateau search, which consists in performing a randomized sequence of swaps.…”

Section: Introductionmentioning

confidence: 99%

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Fast local search for the maximum independent set problem

2012

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Given a graph G = (V , E), the independent set problem is that of finding a maximum-cardinality subset S of V such that no two vertices in S are adjacent. We introduce two fast local search routines for this problem. The first can determine in linear time whether a maximal solution can be improved by replacing a single vertex with two others. The second routine can determine in O(m ) time (where is the highest degree in the graph) whether there are two solution vertices than can be replaced by a set of three. We also present a more elaborate heuristic that successfully applies local search to find near-optimum solutions to a wide variety of instances. We test our algorithms on instances from the literature as well as on new ones proposed in this paper.

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A Stochastic Local Search Approach to Vertex Cover

Cited by 64 publications

References 17 publications

Topological map induction using neighbourhood information of places

Topological map induction using neighbourhood information of places

A review on algorithms for maximum clique problems

Fast local search for the maximum independent set problem

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