Skip to main content
SpringerLink
Log in

A 2log2(n)-Approximation Algorithm for Directed Tour Cover

  • Conference paper
Book cover Combinatorial Optimization and Applications (COCOA 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5573))

Abstract

Given a directed graph G with non-negative cost on the arcs, a directed tour cover T of G is a cycle (not necessary simple) in G such that either head or tail (or both of them) of every arc in G is touched by T. The minimum directed tour cover problem (DToCP) which is to find a directed tour cover of minimum cost, is NP-hard. It is thus interesting to design approximation algorithms with performance guarantee to solve this problem. Although its undirected counterpart (ToCP) has been studied in recent years [1,6], in our knowledge, the DTCP remains widely open. In this paper, we give a 2log2(n)-approximation algorithm for the DTCP.

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 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.00
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.

References

  1. Arkin, E.M., Halldórsson, M.M., Hassin, R.: Approximating the Tree and Tour Covers of a Graph. Information Processing Letters 47, 275–282 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  2. Frieze, A.M., Galbiati, G., Maffioli, F.: On the Worst Case Performance of some Algorithms for the Asymmetric Traveling Salesman problem. Networks 12, 23–39 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  3. Goemans, M.X., Bertsimas, D.J.: On the Parsimonious Property of Connectivity Problems. In: Proc. of the 1st ACM-SIAM Symposimum on Disc. Alg (SODA 1990), pp. 388–396 (1990)

    Google Scholar 

  4. Jackson, B.: Some Remarks on Arc-Connectivity, Vertex Splitting, and Orientation in Graphs and Digraphs. Journal of Graph Theory 12(3), 429–436 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kaplan, H., Lewenstein, M., Shafrir, N., Sviridenko, M.: Approximation Algorithms for Asymmetric TSP by Decomposing Directed Regular multigraphs. J. ACM 52(4), 602–626 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Könemann, J., Konjevod, G., Parekh, O., Sinha, A.: Improved Approximations for Tour and Tree Covers. Algorithmica 38(3), 441–449 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lovasz, L.: On Some Connectivity Properties of Eulerian Graphs. Acta Mathematica Hungarica 28, 129–138 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  8. Williamson, D.P.: Analysis of the Held-Karp Heuristic for the Traveling Salesman Problem. Master Thesis, MIT (1990)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LIP6, Université Pierre et Marie Curie Paris 6, 4 place Jussieu, Paris, France

    Viet Hung Nguyen

  2. LIF, Université de la Mediterrannée, 163 avenue de Luminy, Marseille, France

    Viet Hung Nguyen

Authors
  1. Viet Hung Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Texas at Dallas, 800 West Campbell Road, TX 75080-3021, Richardson, USA

    Ding-Zhu Du

  2. Chinese Academy of Sciences, Institute of Applied Mathematics, Zhong Guan Cun Dong Lu 55, 100190, Beijing, P. R. China

    Xiaodong Hu

  3. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P.O. Box 116595, FL 32611-6595, Gainesville, USA

    Panos M. Pardalos

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nguyen, V.H. (2009). A 2log2(n)-Approximation Algorithm for Directed Tour Cover. In: Du, DZ., Hu, X., Pardalos, P.M. (eds) Combinatorial Optimization and Applications. COCOA 2009. Lecture Notes in Computer Science, vol 5573. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02026-1_19

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02026-1_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02025-4

  • Online ISBN: 978-3-642-02026-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation