Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Graph-Theoretic Concepts in Computer Science

WG 1999: Graph-Theoretic Concepts in Computer Science pp 42–54Cite as

Euler Is Standing in Line

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1665))

Abstract

In this paper we study algorithms for “Dial-a-Ride” transportation problems. In the basic version of the problem we are given transportation jobs between the vertices of a graph and the goal is to find a shortest transportation that serves all the jobs. This problem is known to be NP-hard even on trees. We consider the extension when precedence relations between the jobs with the same source are given. Our results include a polynomial time algorithm on paths and approximation algorithms general graphs and trees with performances of 9/4 and 5/3, respectively.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Networks flows, Prentice Hall, Englewood Cliffs, New Jersey, 1993. 52, 53

    Google Scholar 

  2. N. Ascheuer, M. Grötschel, S. O. Krumke, and J. Rambau, Combinatorial online optimization, Proceedings of the International Conference of Operations Research (OR’98), Springer, 1998, pp. 21–37.

    Google Scholar 

  3. M. J. Atallah and S. R. Kosaraju, Efficient solutions to some transportation problems with applications to minimizing robot arm travel, SIAMJournal on Computing 17 (1988), no. 5, 849–869. 44, 45, 46, 46, 49

    Article  MATH  MathSciNet  Google Scholar 

  4. N. Christofides, Worst-case analysis of a new heuristic for the traveling salesman problem, Tech. report, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, PA, 1976. 52

    Google Scholar 

  5. T. H. Cormen, C. E. Leiserson, and R. L. Rivest, Introduction to algorithms, MIT Press, 1990. 53

    Google Scholar 

  6. G. N. Frederickson and D. J. Guan, Preemptive ensemble motion planning on a tree, SIAM Journal on Computing 21 (1992), no. 6, 1130–1152.

    Article  MATH  MathSciNet  Google Scholar 

  7. G. N. Frederickson and D. J. Guan, Nonpreemptive ensemble motion planning on a tree, Journal of Algorithms 15 (1993), no. 1, 29–60. 43, 44, 45, 45, 45, 46, 46

    Article  MATH  MathSciNet  Google Scholar 

  8. G. N. Frederickson, M. S. Hecht, and C. E. Kim, Approximation algorithms for some routing problems, SIAM Journal on Computing 7 (1978), no. 2, 178–193. 44, 46, 49

    Article  MathSciNet  Google Scholar 

  9. D. J. Guan, Routing a vehicle of capacity greater than one, Discrete Applied Mathematics 81 (1998), no. 1, 41–57.

    Article  MATH  MathSciNet  Google Scholar 

  10. D. Harel and R. E. Tarjan, Fast algorithms for finding nearest common ancestors, SIAM Journal on Computing 13 (1984), no. 2, 338–355. 53

    Article  MATH  MathSciNet  Google Scholar 

  11. B. Schieber and U. Vishkin, On finding lowest common ancestors: Simplification and parallelization, SIAM Journal on Computing 17 (1988), no. 6, 1253–1262. 53

    Article  MATH  MathSciNet  Google Scholar 

  12. R. E. Tarjan, Finding optimum branchings, Networks 7 (1977), 25–35. 49, 53

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Würzburg, Am Hubland, 97074, Würzburg, Germany

    D. Hauptmeier, S. O. Krumke & J. Rambau

  2. Department Optimization, Konrad-Zuse-Zentrum für Informationstechnik Berlin, Takustr. 7, 14195, Berlin-Dahlem, Germany

    H.-C. Wirth

Authors
  1. D. Hauptmeier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. O. Krumke
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. Rambau
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H.-C. Wirth
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Theoretical Computer Science ETH Zürich ETH Zentrum, 8092, Zürich, Switzerland

    Peter Widmayer , Gabriele Neyer  & Stephan Eidenbenz ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hauptmeier, D., Krumke, S.O., Rambau, J., Wirth, HC. (1999). Euler Is Standing in Line. In: Widmayer, P., Neyer, G., Eidenbenz, S. (eds) Graph-Theoretic Concepts in Computer Science. WG 1999. Lecture Notes in Computer Science, vol 1665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46784-X_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-46784-X_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66731-5

  • Online ISBN: 978-3-540-46784-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation