Algorithmica

, Volume 15, Issue 6, pp 521–549

Algorithms for dense graphs and networks on the random access computer

  • J. Cheriyan
  • K. Mehlhorn
Article

DOI: 10.1007/BF01940880

Cite this article as:
Cheriyan, J. & Mehlhorn, K. Algorithmica (1996) 15: 521. doi:10.1007/BF01940880
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Abstract

We improve upon the running time of several graph and network algorithms when applied to dense graphs. In particular, we show how to compute on a machine with word size λ=Ω (logn) a maximal matching in ann-vertex bipartite graph in timeO(n2+n2.5/λ)=O(n2.5/logn), how to compute the transitive closure of a digraph withn vertices andm edges in timeO(n2+nm/λ), how to solve the uncapacitated transportation problem with integer costs in the range [O.C] and integer demands in the range [−U.U] in timeO ((n3 (log log/logn)1/2+n2 logU) lognC), and how to solve the assignment problem with integer costs in the range [O.C] in timeO(n2.5 lognC/(logn/loglogn)1/4).

Assuming a suitably compressed input, we also show how to do depth-first and breadth-first search and how to compute strongly connected components and biconnected components in timeO(nλ+n2/λ), and how to solve the single source shortest-path problem with integer costs in the range [O.C] in time0 (n2(logC)/logn). For the transitive closure algorithm we also report on the experiences with an implementation.

Key words

Graph Network Algorithm Dense graph Dense network 

Copyright information

© Springer-Verlag New York Inc 1996

Authors and Affiliations

  • J. Cheriyan
    • 1
  • K. Mehlhorn
    • 2
  1. 1.Department of Combinatorics and OptimizationUniversity of WaterlooWaterlooCanada
  2. 2.Max-Planck-Institut für Informatik and Universität des SaarlandesSaarbrückenGermany

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