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Exponential Time Approximation Scheme for TSP

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Algorithmic Aspects in Information and Management (AAIM 2019)

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Abstract

In this paper, we develop an exponential time approximation scheme for the traveling salesman problem (TSP) on undirected graphs. If the weight of each edge is a nonnegative real number, then there is an algorithm to give an \((1+\epsilon )\) approximation for the TSP problem in \(O({1\over \epsilon }\cdot 1.66^n)\) and a polynomial space. It is in contrast to Golovnen’s approximation scheme for TSP on directed graphs with \(\mathrm{O}({1\over \epsilon }\cdot 2^n)\) time. We also show that there is no \(2^{o(n)}\) time constant factor approximation for the TSP problem under Exponential Time Hypothesis in complexity theory.

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Acknowledgments

The authors would like to thank the reviewers whose suggestions improve the presentation of this paper. This research is supported by NSFC 61772179, NSFC 61872450 and Hunan Provincial Natural Science Foundation 2019JJ40005.

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Authors and Affiliations

  1. Department of Computer Science, University of Texas Rio Grande Valley, Edinburg, TX, 78539, USA

    Zhixiang Chen & Bin Fu

  2. School of Information, Central Southern University, Changsha, China

    Qilong Feng & Jianxin Wang

  3. School of Computer Science and Technology, Hengyang Normal University, Hengyang, China

    Mugang Lin

Authors
  1. Zhixiang Chen
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  2. Qilong Feng
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  3. Bin Fu
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  4. Mugang Lin
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  5. Jianxin Wang
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Corresponding author

Correspondence to Bin Fu .

Editor information

Editors and Affiliations

  1. The University of Texas at Dallas, Richardson, TX, USA

    Ding-Zhu Du

  2. Hefei University of Technology, Hefei, China

    Lian Li

  3. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Xiaoming Sun

  4. Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

    Jialin Zhang

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Chen, Z., Feng, Q., Fu, B., Lin, M., Wang, J. (2019). Exponential Time Approximation Scheme for TSP. In: Du, DZ., Li, L., Sun, X., Zhang, J. (eds) Algorithmic Aspects in Information and Management. AAIM 2019. Lecture Notes in Computer Science(), vol 11640. Springer, Cham. https://doi.org/10.1007/978-3-030-27195-4_11

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  • DOI: https://doi.org/10.1007/978-3-030-27195-4_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-27194-7

  • Online ISBN: 978-3-030-27195-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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