Towards faster local search for minimum weight vertex cover on massive graphs

Inf. Sci., Volume 471, 2019, Pages 64-79.

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np hardefficient local search algorithmreal worldmwvc problemconstruction procedureMore(12+)
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We developed a new local search algorithm for minimum weight vertex cover problem called FastWVC, which works well for massive graphs

Abstract:

Abstract The minimum weight vertex cover (MWVC) problem is a well known NP-hard problem with various real-world applications. In this paper, we design an efficient algorithm named FastWVC to solve MWVC problem in massive graphs. To this end, we propose a construction procedure, which aims to generate a quality initial vertex cover in sh...More

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Introduction
  • The minimum vertex cover (MVC) problem is to find a minimum sized vertex cover in a graph, where a vertex cover is a subset of vertices that contains at least one endpoint of each edge.
  • The minimum weight vertex cover (MWVC) problem is a 5 generalization of MVC.
  • In a vertex weighted graph, each vertex has a positive weight and the purpose of the MWVC problem is to find a vertex cover with the minimum weight.
  • The MVC problem is NP hard
  • It is NP-hard to approximate MVC 10 within any factors smaller than 1.3606 [6].
  • Due to the computational intractability of the MVC problem, various heuristic algorithms have been proposed to find approximate solutions within reasonable time.
Highlights
  • The minimum vertex cover (MVC) problem is to find a minimum sized vertex cover in a graph, where a vertex cover is a subset of vertices that contains at least one endpoint of each edge
  • We develop a local search algorithm named FastWVC
  • We propose a new exchange step for our algorithm
  • The weight of each vertex is assigned to a value from [20,100] uniformly at random, as with the generation method adopted in testing DLSWCC [10]
  • We developed a new local search algorithm for minimum weight vertex cover (MWVC) problem called FastWVC, which works well for massive graphs
  • We carried out extensive experiments to compare FastWVC with state-of-the-art algorithms on a board range of benchmarks from real world networks
Results
  • Experimental results in Section

    6 will confirm its effectiveness.

    250 5.
  • The FastWVC Algorithm.
  • The authors present the FastWVC algorithm and give a detailed description.
  • The initial solution C is constructed by ConstructWVC.
  • The best found solution C∗ is initialized as C.
  • The weight of each edge is set to 1 , con fChange(v) is set to.
  • The authors compare FastWVC with three state-of-the-art algorithms, and show that the algorithm has better performance.
  • The weight of each vertex is assigned to a value from [20,100] uniformly at random, as with the generation method adopted in testing DLSWCC [10]
Conclusion
  • Conclusions and Future Work

    In this paper, the authors developed a new local search algorithm for MWVC problem called FastWVC, which works well for massive graphs.
  • The authors would like to further improve the algorithm by low complexity strategies for large 405 graphs
Summary
  • Introduction:

    The minimum vertex cover (MVC) problem is to find a minimum sized vertex cover in a graph, where a vertex cover is a subset of vertices that contains at least one endpoint of each edge.
  • The minimum weight vertex cover (MWVC) problem is a 5 generalization of MVC.
  • In a vertex weighted graph, each vertex has a positive weight and the purpose of the MWVC problem is to find a vertex cover with the minimum weight.
  • The MVC problem is NP hard
  • It is NP-hard to approximate MVC 10 within any factors smaller than 1.3606 [6].
  • Due to the computational intractability of the MVC problem, various heuristic algorithms have been proposed to find approximate solutions within reasonable time.
  • Results:

    Experimental results in Section

    6 will confirm its effectiveness.

    250 5.
  • The FastWVC Algorithm.
  • The authors present the FastWVC algorithm and give a detailed description.
  • The initial solution C is constructed by ConstructWVC.
  • The best found solution C∗ is initialized as C.
  • The weight of each edge is set to 1 , con fChange(v) is set to.
  • The authors compare FastWVC with three state-of-the-art algorithms, and show that the algorithm has better performance.
  • The weight of each vertex is assigned to a value from [20,100] uniformly at random, as with the generation method adopted in testing DLSWCC [10]
  • Conclusion:

    Conclusions and Future Work

    In this paper, the authors developed a new local search algorithm for MWVC problem called FastWVC, which works well for massive graphs.
  • The authors would like to further improve the algorithm by low complexity strategies for large 405 graphs
Tables
  • Table1: Experiment results on massive graphs
  • Table2: Experiment results on massive graphs (continued)
  • Table3: Results of ConstructWVC and ConstructWVC1
  • Table4: Results of ConstructWVC and ConstructWVC1 (continued)
  • Table5: Comparison results of FastWVC, FastWVC1 and FastWVC2
  • Table6: Comparison results of FastWVC, FastWVC1 and FastWVC2 (continued)
  • Table7: Comparison results of FastWVC and FastWVC3 instance
  • Table8: Comparison results of FastWVC and FastWVC3 (continued)
Download tables as Excel
Funding
  • This work is supported by National Natural Science Foundation of China 61502464
  • Shaowei Cai is also supported by Youth Innovation Promotion Association, Chinese Academy of Sciences
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