Skip to main content
SpringerLink
Log in

Reoptimization of Minimum and Maximum Traveling Salesman’s Tours

  • Conference paper
Algorithm Theory – SWAT 2006 (SWAT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4059))

Included in the following conference series:

Abstract

In this paper, reoptimization versions of the traveling salesman problem (TSP) are addressed. Assume that an optimum solution of an instance is given and the goal is to determine if one can maintain a good solution when the instance is subject to minor modifications. We study the case where nodes are inserted in, or deleted from, the graph. When inserting a node, we show that the reoptimization problem for MinTSP is approximable within ratio 4/3 if the distance matrix is metric. We show that, dealing with metric MaxTSP, a simple heuristic is asymptotically optimum when a constant number of nodes are inserted. In the general case, we propose a 4/5-approximation algorithm for the reoptimization version of MaxTSP.

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.

References

  1. Archetti, C., Bertazzi, L., Speranza, M.G.: Reoptimizing the traveling salesman problem. Networks 42(3), 154–159 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bartusch, M., Mohring, R.H., Radermacher, F.J.: Scheduling project networks with resource constraints and time windows. Ann. Oper. Res. 16, 201–240 (1988)

    Article  MathSciNet  Google Scholar 

  3. Bartusch, M., Mohring, R.H., Radermacher, F.J.: A conceptional outline of a dss for scheduling problems in the building industry. Decision Support Systems 5, 321–344 (1989)

    Article  Google Scholar 

  4. Chen, Z.-Z., Okamoto, Y., Wang, L.: Improved deterministic approximation algorithms for Max TSP. Information Processessing Letters 95, 333–342 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Christofides, N.: Worst-case analysis of a new heuristic for the traveling salesman problem. Technical Report 338, Grad School of Industrial Administration, Canergi-Mellon University, Pittsburgh (1976)

    Google Scholar 

  6. Eppstein, D., Galil, Z., Italiano, G.F., Nissenzweig, A.: Sparsification - a technique for speeding up dynamic graph algorithms. Journal of the ACM 44(5), 669–696 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  7. Gutin, G., Punnen, A.P.: The Traveling Salesman Problem and Its Variations. Combinatorial Optimization. Kluwer Academic Publishers, Dordrecht (2002)

    MATH  Google Scholar 

  8. Hartvigsen, D.: Extensions of Matching Theory. PhD thesis, Carnegie-Mellon University (1984)

    Google Scholar 

  9. Hassin, R., Rubinstein, S.: A 7/8-approximation algorithm for metric Max TSP. Information Processessing Letters 81(5), 247–251 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  10. Henzinger, M.R., King, V.: Maintaining minimum spanning trees in dynamic graphs. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256, pp. 594–604. Springer, Heidelberg (1997)

    Google Scholar 

  11. Johnson, D.S., McGeoch, L.A.: The traveling salesman problem: a case study. In: Aarts, E., Lenstra, J.K. (eds.) Local search in combinatorial optimization. Wiley, Chichester (1997)

    Google Scholar 

  12. Lawler, E.L., Lenstra, J.K., Rinnooy Kan, A.H.G., Shmoys, D.B.: The Traveling Salesman Problem: a guided tour of Combinatorial Optimization. In: Discrete Mathematics and Optimization. Wiley, Chichester (1985)

    Google Scholar 

  13. Papadimitriou, C.H., Steiglitz, K.: Some complexity results for the traveling salesman problem. In: STOC 1976, pp. 1–9 (1976)

    Google Scholar 

  14. Papadimitriou, C.H., Yannakakis, M.: The traveling salesman problem with distances one and two. Mathematics of Operations Research 18, 1–11 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  15. Rosenkrantz, D.J., Stearns, R.E., Lewis II, P.M.: An analysis of several heuristics for the traveling salesman problem. SIAM J. Comput. 6(3), 563–581 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  16. Sahni, S., Gonzalez, T.F.: P-complete approximation problems. J. ACM 23(3), 555–565 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  17. Schäffter, M.W.: Scheduling with forbidden sets. Discrete Applied Mathematics 72(1-2), 155–166 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  18. Serdyukov, A.I.: An algorithm with an estimate for the traveling salesman problem of the maximum. Upravlyaemye Sistemy (in Russian) 25, 80–86 (1984)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, Roma, Italy

    Giorgio Ausiello

  2. Lamsade, CNRS and Université Paris Dauphine, France

    Bruno Escoffier, Jérôme Monnot & Vangelis Th. Paschos

Authors
  1. Giorgio Ausiello
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bruno Escoffier
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jérôme Monnot
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vangelis Th. Paschos
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. MADALGO, Department of Computer Science, University of Aarhus, Denmark

    Lars Arge

  2. Institute of Mathematics and Computer Science, University of Latvia, Raiņa bulvāris 29, Rīga, LV-1459, Latvia

    Rusins Freivalds

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ausiello, G., Escoffier, B., Monnot, J., Paschos, V.T. (2006). Reoptimization of Minimum and Maximum Traveling Salesman’s Tours. In: Arge, L., Freivalds, R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785293_20

Download citation

  • DOI: https://doi.org/10.1007/11785293_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35753-7

  • Online ISBN: 978-3-540-35755-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation