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An Exact Algorithm for TSP in Degree-3 Graphs via Circuit Procedure and Amortization on Connectivity Structure

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Theory and Applications of Models of Computation (TAMC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7876))

Abstract

The paper presents an O *(1.2312n)-time and polynomial-space algorithm for the traveling salesman problem in an n-vertex graph with maximum degree 3. This improves the previous time bound for this problem. Our algorithm is a simple branch-and-search algorithm. The only branch rule is designed on a cut-circuit structure of a graph induced by unprocessed edges. To improve a time bound by a simple analysis on measure and conquer, we introduce an amortization scheme over the cut-circuit structure by defining the measure of an instance to be the sum of not only weights of vertices but also weights of connected components of the induced graph.

Supported by National Natural Science Foundation of China under the Grant 60903007 and Fundamental Research Funds for the Central Universities under the Grant ZYGX2012J069.

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Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, University of Electronic Science and Technology of China, China

    Mingyu Xiao

  2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan

    Hiroshi Nagamochi

Authors
  1. Mingyu Xiao
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  2. Hiroshi Nagamochi
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Editor information

Editors and Affiliations

  1. The University of Hong Kong, Hong Kong

    T-H. Hubert Chan

  2. The Chinese University of Hong Kong, Hong Kong

    Lap Chi Lau

  3. Department of Computer Science, Stanford University, 94305, Stanford, CA, USA

    Luca Trevisan

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Xiao, M., Nagamochi, H. (2013). An Exact Algorithm for TSP in Degree-3 Graphs via Circuit Procedure and Amortization on Connectivity Structure. In: Chan, TH.H., Lau, L.C., Trevisan, L. (eds) Theory and Applications of Models of Computation. TAMC 2013. Lecture Notes in Computer Science, vol 7876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38236-9_10

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  • DOI: https://doi.org/10.1007/978-3-642-38236-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38235-2

  • Online ISBN: 978-3-642-38236-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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