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International Workshop on Frontiers in Algorithmics

FAW 2018: Frontiers in Algorithmics pp 286–299Cite as

A Method to Compute the Sparse Graphs for Traveling Salesman Problem Based on Frequency Quadrilaterals

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10823))

Abstract

In this paper, an iterative algorithm is designed to compute the sparse graphs for traveling salesman problem (TSP) according to the frequency quadrilaterals so that the computation time of the algorithms for TSP will be lowered. At each computation cycle, the algorithm first computes the average frequency \( \overline{f} (e) \) of an edge e with N frequency quadrilaterals containing e in the input graph G(V, E). Then the 1/3|E| edges with low frequency are eliminated to generate the output graph with a smaller number of edges. The algorithm can be iterated several times and the original optimal Hamiltonian cycle is preserved with a high probability. The experiments demonstrate the algorithm computes the sparse graphs with the O(nlog2 n) edges containing the original optimal Hamiltonian cycle for most of the TSP instances in the TSPLIB. The computation time of the iterative algorithm is O(Nn 2).

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Acknowledgement

The authors acknowledge the anonymous referees for their suggestions to improve the paper. We acknowledge W. Cook, H. Mittelmann who created the Concorde and G. Reinelt, et al. who provided the TSP data to TSPLIB. The authors acknowledge the funds supported by NSFC (No. 51205129) and the Fundamental Research Funds for the Central Universities (No. 2015ZD10). We also thank the support of Beijing Key Laboratory of Energy Safety and Clean Utilization.

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Authors and Affiliations

  1. North China Electric Power University, Beijing, 102206, China

    Yong Wang

  2. University of California, San Diego, CA, 92093, USA

    Jeffrey Remmel

Authors
  1. Yong Wang
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  2. Jeffrey Remmel
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Correspondence to Yong Wang .

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Editors and Affiliations

  1. Texas A&M University, College Station, Texas, USA

    Jianer Chen

  2. Shanghai University of Finance and Economics, Shanghai, China

    Pinyan Lu

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Wang, Y., Remmel, J. (2018). A Method to Compute the Sparse Graphs for Traveling Salesman Problem Based on Frequency Quadrilaterals. In: Chen, J., Lu, P. (eds) Frontiers in Algorithmics. FAW 2018. Lecture Notes in Computer Science(), vol 10823. Springer, Cham. https://doi.org/10.1007/978-3-319-78455-7_22

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  • DOI: https://doi.org/10.1007/978-3-319-78455-7_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78454-0

  • Online ISBN: 978-3-319-78455-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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