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Algorithmica

, Volume 17, Issue 1, pp 67–87 | Cite as

Parallel algorithms for the hamiltonian cycle and hamiltonian path problems in semicomplete bipartite digraphs

  • J. Bang-Jensen
  • M. El Haddad
  • Y. Manoussakis
  • T. M. Przytycka
Article

Abstract

We give anO(log4 n)-timeO(n 2)-processor CRCW PRAM algorithm to find a hamiltonian cycle in a strong semicomplete bipartite digraph,B, provided that a factor ofB (i.e., a collection of vertex disjoint cycles covering the vertex set ofB) is computed in a preprocessing step. The factor is found (if it exists) using a bipartite matching algorithm, hence placing the whole algorithm in the class Random-NC.

We show that any parallel algorithm which can check the existence of a hamiltonian cycle in a strong semicomplete bipartite digraph in timeO(r(n)) usingp(n) processors can be used to check the existence of a perfect matching in a bipartite graph in timeO(r(n)+n 2 /p(n)) usingp(n) processors. Hence, our problem belongs to the class NC if and only if perfect matching in bipartite graphs belongs to NC.

We also consider the problem of finding a hamiltonian path in a semicomplete bipartite digraph.

Key Words

Graph algorithms Hamilton cycle Parallel algorithms Semicomplete bipartite graphs Randomized algorithms 

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Copyright information

© Springer-Verlag New York Inc 1997

Authors and Affiliations

  • J. Bang-Jensen
    • 1
  • M. El Haddad
    • 2
  • Y. Manoussakis
    • 2
  • T. M. Przytycka
    • 1
  1. 1.Department of Mathematics and Computer ScienceOdense UniversityOdense MDenmark
  2. 2.Université de Paris-Sud OrsayOrsay CedexFrance

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