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

Information Sciences, pp. 64-79, 2019.

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Keywords:

Minimum weighted vertex coverLocal searchMassive graph

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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 short time. W...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

- 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)

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

Reference

- Bouamama, S., Blum, C., & Boukerram, A. (2012). A population-based iterated greedy algorithm for the minimum weight vertex cover problem. Appl. Soft Comput., 12, 1632–1639.
- Cai, S. (2015). Balance between complexity and quality: local search for minimum vertex cover in massive graphs. In Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence, IJCAI 2015, Buenos Aires, Argentina, July 25-31, 2015 (pp. 747–753).
- Cai, S., Su, K., Luo, C., & Sattar, A. (2013). NuMVC: an efficient local search algorithm for minimum vertex cover. Journal of Artificial Intelligence Research, 46, 687–716.
- Cai, S., Su, K., & Sattar, A. (2011). Local search with edge weighting and configuration checking heuristics for minimum vertex cover. Artificial Intelligence, 175, 1672–1696.
- Chvatal, V. (1979). A greedy heuristic for the set-covering problem. Mathematics of Operations Research, 4, 233–235.
- Dinur, I., & Safra, S. (2005). On the hardness of approximating minimum vertex cover. Annals of Mathematics, 162, 439–485.
- Glover, F. (1989). Tabu search – part i. ORSA Journal on Computing, 1, 190–206.
- Jovanovic, R., & Tuba, M. (2011). An ant colony optimization algorithm with improved pheromone correction strategy for the minimum weight vertex cover problem. Applied Soft Computing, 11, 5360–5366.
- Katzmann, M., & Komusiewicz, C. (2017). Systematic exploration of larger local search neighborhoods for the minimum vertex cover problem. In Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, February 4-9, 2017, San Francisco, California, USA. (pp. 846–852).
- Li, R., Hu, S., Zhang, H., & Yin, M. (2016). An efficient local search framework for the minimum weighted vertex cover problem. Information Sciences, 372, 428–445.
- Li, Y., Cai, S., & Hou, W. (2017). An efficient local search algorithm for minimum weighted vertex cover on massive graphs. In Proceedings of 11th International Conference of Simulated Evolution and Learning, SEAL 2017, Shenzhen, China, November 10-13, 2017, (pp. 145–157).
- Ma, Z., Fan, Y., Su, K., Li, C., & Sattar, A. (2016). Random walk in large realworld graphs for finding smaller vertex cover. In IEEE International Conference on TOOLS with Artificial Intelligence (pp. 686–690).
- Ni, Y. (2012). Minimum weight covering problems in stochastic environments. Information Sciences, 214, 91–104.
- Nogueira, B., Pinheiro, R. G. S., & Subramanian, A. (2018). A hybrid iterated local search heuristic for the maximum weight independent set problem. Optimization Letters, 12, 567–583.
- Richter, S., Helmert, M., & Gretton, C. (2007). A stochastic local search approach to vertex cover. In Proceedings of KI-07 (pp. 412–426).
- Rossi, R. A., & Ahmed, N. K. (2015). The network data repository with interactive graph analytics and visualization. In Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence. URL: http://networkrepository.com.
- Shyu, S. J., Yin, P. Y., & Lin, B. M. T. (2004). An ant colony optimization algorithm for the minimum weight vertex cover problem. Annals of Operations Research, 131, 283–304.
- Singh, A., & Gupta, A. K. (2011). A hybrid heuristic for the minimum weight vertex cover problem. Asia-Pacific Journal of Operational Research (APJOR), 23, 273–285.
- Wagner, M., Friedrich, T., & Lindauer, M. (2017). Improving local search in a minimum vertex cover solver for classes of networks. In 2017 IEEE Congress on Evolutionary Computation, CEC 2017, Donostia, San Sebastian, Spain, June 5-8, 2017 (pp. 1704–1711).
- Zhou, T., Zhipeng, Wang, Y., Ding, J., & Peng, B. (2016). Multi-start iterated tabu search for the minimum weight vertex cover problem. Journal of Combinatorial Optimization, 32, 368–384.

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