Linear Time Algorithms on Chordal Bipartite and Strongly Chordal Graphs

  • Ryuhei Uehara
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2380)

Abstract

Chordal bipartite graphs are introduced to analyze nonsymmetric matrices, and form a large class of perfect graphs. There are several problems, which can be solved efficiently on the class using the characterization by the doubly lexical ordering of the bipartite adjacency matrix. However, the best known algorithm for computing the ordering runs in O(minm log n, n2), which is the bottleneck of the problems. We show a linear time algorithm that computes the ordering of a given chordal bipartite graph. The result improves the upper bounds of several problems, including recognition problem, from O(minm log n, n2) to linear time. Strongly chordal graphs are well-studied subclass of chordal graphs, and that have similar characterization. The upper bounds of several problems on a given strongly chordal graph are also improved from O(minm log n, n2) to linear time.

Keywords

Chordal bipartite graphs design and analysis of algorithms lexicographic breadth first search vertex elimination ordering strongly chordal graphs 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Ryuhei Uehara
    • 1
  1. 1.Natural Science FacultyKomazawa UniversityJapan

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