Skip to main content
SpringerLink
Log in

An Improved Exact Algorithm for TSP in Degree-4 Graphs

  • Conference paper
Computing and Combinatorics (COCOON 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7434))

Included in the following conference series:

Abstract

The paper presents an O *(1.716n)-time polynomial-space algorithm for the traveling salesman problem in an n-vertex edge-weighted graph with maximum degree 4, which improves the previous results of the O *(1.890n)-time polynomial-space algorithm by Eppstein and the O *(1.733n)-time exponential-space algorithm by Gebauer.

Supported in part by Grant 60903007 of NSFC, China.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Bjorklund, A.: Determinant sums for undirected Hamiltonicity. In: Proc. 51st Annual IEEE Symp. on Foundations of Computer Science, pp. 173–182 (2010)

    Google Scholar 

  2. Bjorklund, A., Husfeldt, T., Kasaki, P., Koivisto, M.: The Travelling Salesman Problem in Bounded Degree Graphs. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 198–209. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  3. Dorn, F., Penninkx, E., Bodlaender, H.L., Fomin, F.V.: Efficient exact algorithms on planar graphs: Exploiting sphere cut decompositions. Algorithmica 58(3), 790–810 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  4. Eppstein, D.: Quasiconvex analysis of multivariate recurrence equations for backtracking algorithms. ACM Trans. on Algorithms 2(4), 492–509 (2006)

    Article  MathSciNet  Google Scholar 

  5. Eppstein, D.: The traveling salesman problem for cubic graphs. J. Graph Algorithms and Applications 11(1), 61–81 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  6. Gebauer, H.: Finding and enumerating Hamilton cycles in 4-regular graphs. Theoretical Computer Science 412(35), 4579–4591 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  7. Iwama, K., Nakashima, T.: An Improved Exact Algorithm for Cubic Graph TSP. In: Lin, G. (ed.) COCOON 2007. LNCS, vol. 4598, pp. 108–117. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Woeginger, G.J.: Exact Algorithms for NP-hard Problems: A Survey. In: Jünger, M., Reinelt, G., Rinaldi, G. (eds.) Combinatorial Optimization - Eureka, You Shrink! LNCS, vol. 2570, pp. 185–207. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Mingyu Xiao

  2. Graduate School of Informatics, Kyoto University, Japan

    Hiroshi Nagamochi

Authors
  1. Mingyu Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hiroshi Nagamochi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of IT, University of Sydney, Building J12, 2006, Sydney, NSW, Australia

    Joachim Gudmundsson , Julián Mestre  & Taso Viglas ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Xiao, M., Nagamochi, H. (2012). An Improved Exact Algorithm for TSP in Degree-4 Graphs. In: Gudmundsson, J., Mestre, J., Viglas, T. (eds) Computing and Combinatorics. COCOON 2012. Lecture Notes in Computer Science, vol 7434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32241-9_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-32241-9_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32240-2

  • Online ISBN: 978-3-642-32241-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation