Skip to main content
SpringerLink
Log in

Optimal parallel computations for halin graphs

  • Conference paper
  • First Online:
Optimal Algorithms (OA 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 401))

Included in the following conference series:

  • 153 Accesses

Abstract

Optimal parallel algorithms are given for two hard problems (the Hamiltonian cycle and the travelling salesman problem) restricted to graphs having a simple structure — Halin graphs. These problems were previously investigated for Halin graphs from the sequential point of view [1,5,6]. The travelling salesman problem (the computation of the shortest Hamiltonian cycle) for the Halin graph is interesting because such a graph can contain an exponential number of Hamiltonian cycles. Two tree-oriented algorithmic techniques are used: computation of products for paths of the tree (which gives log2n time algorithm for the Hamiltonian cycle) and a special parallel pebble game (giving log2n time for the travelling salesman problem).

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. G. Cornnuejols, D. Nadoff, W. Pullybank. Halin graphs and the travelling salesman problem. Math.Progr. 26 (1983) 287–294

    Google Scholar 

  2. A. Gibbons, W.Rytter. Efficient parallel algorithms. Cambridge University Press (1988)

    Google Scholar 

  3. A. Gibbons, W. Rytter. Optimal parallel algorithms for dynamic expression evaluation and context-free recognition. Information and Computation 81 (1989), 32–45.

    Google Scholar 

  4. W. Rytter. Fast parallel omputations for some dynamic programming problems. Theor. Computer Science (1988)

    Google Scholar 

  5. M.Syslo. NP-complete problems on some tree structured graphs. WG'83 (ed. M. Nagl).

    Google Scholar 

  6. M. Syslo, A. Proskurowski. On Halin graphs, in M. Borowiecki, J.W. Kennedy, M. Syslo (Editors), Graph Theory-Lagow 1981, LN in Maths, Springer-Verlag, Berlin-Heidelberg, 1983.

    Google Scholar 

  7. R.E. Tarjan, U. Vishkin, An Efficient Parallel Biconnectivity Algorithm, SIAM J.Comput. 14:4(1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Instytut Informatyki, Uniwersytet Warszawski, PKiN, 8p., pok. 850, 00-901, Warszawa, Poland

    Krzysztof Diks & Wojciech Rytter

Authors
  1. Krzysztof Diks
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wojciech Rytter
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hristo Djidjev

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Diks, K., Rytter, W. (1989). Optimal parallel computations for halin graphs. In: Djidjev, H. (eds) Optimal Algorithms. OA 1989. Lecture Notes in Computer Science, vol 401. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51859-2_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-51859-2_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-51859-4

  • Online ISBN: 978-3-540-46831-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation