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

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

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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

- 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

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