Computing

, Volume 56, Issue 4, pp 397–401 | Cite as

A fast algorithm for a class of bottleneck problems

  • A. P. Punnen
Short Communication

Abstract

We show that if a bottleneck problem of sizem with an ordered list of element costs can be solved in O(ξ(m)) time, then the problem with an unordered list of element costs can be solved in O(ξ(m)) log*m) time.

AMS Subject Classifications

90C27 90C35 

Key words

Bottleneck problems polynomial algorithms combinatorial optimization 

Ein schneller Algorithmus für eine Klasse von Engpaß-Problemen

Zusammenfassung

Wenn ein Engpaß-Problem der Größem mit sortierten Kostenkoeffizienten in O(ξ(m)) Zeit gelöst werden kann, dann kann das entsprechende allgemeine Problem in O(ξ(m) log*m) Zeit gelöst werden.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Aho, A., Hopcroft, J. E., Ullman, J. D.: The design and analysis of computer algorithms. Reading: Addison-Wesley 1974.Google Scholar
  2. [2]
    Armstrong, R. D., Jin, Z.: Solving linear bottleneck assignment problem via strong spanning trees. Oper. Res. Lett.12, 179–180 (1992).CrossRefGoogle Scholar
  3. [3]
    Camereni, P. M.: The minimax spanning tree problem and some extensions, Inf. Proc. Lett.7, 10–14 (1978).CrossRefGoogle Scholar
  4. [4]
    Derigs, U., Zimmerman, U.: An augmenting path method for solving linear bottleneck assignment problems. Computing19, 285–298 (1978).CrossRefGoogle Scholar
  5. [5]
    Edmonds, J., Fulkerson, D. R.: Bottleneck extrema. J. Comb. Theory8, 299–306 (1970).Google Scholar
  6. [6]
    Gabow, H. N., Tarjan, R. E.: Algorithms for two bottleneck optimization problems. Algorithms9, 411–417 (1988).CrossRefGoogle Scholar
  7. [7]
    Garfinkel, R. S., Gilbert, K. C.: The bottleneck traveling salesman problem: algorithms and probabilistic analysis. J. ACM25, 435–448 (1978).CrossRefGoogle Scholar
  8. [8]
    Punnen, A. P., Nair, K. P. K.: A fast and simple algorithm for the bottleneck biconnected spanning subgraph problem. Inf. Proc. Lett.50, 283–286 (1994).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • A. P. Punnen
    • 1
  1. 1.Department of Mathematics, Statistics and Computer ScienceUniversity of New BrunswickSaint JohnCanada

Personalised recommendations