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The Polynomial Randomized Algorithm to Compute Bounded Degree Graph for TSP Based on Frequency Quadrilaterals

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Theoretical Computer Science (NCTCS 2022)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1693))

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Abstract

It is the first time that bounded degree graph is proven to be computed for a big class of TSP in polynomial time based on frequency quadrilaterals. As TSP conforms to the properties of frequency quadrilaterals, a polynomial algorithm is given to reduce complete graph of TSP to bounded degree graph in which the optimal Hamiltonian cycle is preserved with a probability above 0.5. For TSP on such bounded degree graphs, there are more competitive exact and approximation algorithms.

Supported by State Key Lab of Alternate Electrical Power System with Renewable Energy Sources, China.

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Author information

Authors and Affiliations

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

    Yong Wang

  2. Tarim University, Alar, 843300, Xinjiang, China

    Yong Wang

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  1. Yong Wang
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Correspondence to Yong Wang .

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Editors and Affiliations

  1. National University of Defense Technology, Changsha, China

    Zhiping Cai

  2. Shanghai Jiao Tong University, Shanghai, China

    Yijia Chen

  3. Chinese Academy of Sciences, Beijing, China

    Jialin Zhang

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Wang, Y. (2022). The Polynomial Randomized Algorithm to Compute Bounded Degree Graph for TSP Based on Frequency Quadrilaterals. In: Cai, Z., Chen, Y., Zhang, J. (eds) Theoretical Computer Science. NCTCS 2022. Communications in Computer and Information Science, vol 1693. Springer, Singapore. https://doi.org/10.1007/978-981-19-8152-4_5

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  • DOI: https://doi.org/10.1007/978-981-19-8152-4_5

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-19-8151-7

  • Online ISBN: 978-981-19-8152-4

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