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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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Abstract

The paper presents an \(O^*(1.2312^n)\)-time and polynomial-space algorithm for the traveling salesman problem in an \(n\)-vertex graph with maximum degree 3. This improves all previous time bounds of polynomial-space algorithms for this problem. Our algorithm is a simple branch-and-search algorithm with only one branch rule 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.

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Authors and Affiliations

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

    Mingyu Xiao

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

    Hiroshi Nagamochi

Authors
  1. Mingyu Xiao
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  2. Hiroshi Nagamochi
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Correspondence to Mingyu Xiao.

Additional information

Supported by National Natural Science Foundation of China under the Grant 61370071 and Fundamental Research Funds for the Central Universities under the Grant ZYGX2012J069.

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Xiao, M., Nagamochi, H. An Exact Algorithm for TSP in Degree-3 Graphs Via Circuit Procedure and Amortization on Connectivity Structure. Algorithmica 74, 713–741 (2016). https://doi.org/10.1007/s00453-015-9970-4

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  • DOI: https://doi.org/10.1007/s00453-015-9970-4

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