BIT Numerical Mathematics

, Volume 34, Issue 4, pp 484–509

Finding minimum height elimination trees for interval graphs in polynomial time

  • Bengt Aspvall
  • Pinar Heggernes
Article

DOI: 10.1007/BF01934264

Cite this article as:
Aspvall, B. & Heggernes, P. BIT (1994) 34: 484. doi:10.1007/BF01934264

Abstract

The elimination tree plays an important role in many aspects of sparse matrix factorization. The height of the elimination tree presents a rough, but usually effective, measure of the time needed to perform parallel elimination. Finding orderings that produce low elimination is therefore important. As the problem of finding minimum height elimination tree orderings is NP-hard, it is interesting to concentrate on limited classes of graphs and find minimum height elimination trees for these efficiently. In this paper, we use clique trees to find an efficient algorithm for interval graphs which make an important subclass of chordal graphs. We first illustrate this method through an algorithm that finds minimum height elimination for chordal graphs. This algorithm, although of exponential time complexity, is conceptionally simple and leads to a polynomial-time algorithm for finding minimum height elimination trees for interval graphs.

AMS subject classifications

05C5065F5065Y05

Key words

Sparse matrix computationelimination treesparallel computinginterval graphs

Copyright information

© the BIT Foundation 1994

Authors and Affiliations

  • Bengt Aspvall
    • 1
  • Pinar Heggernes
    • 1
  1. 1.Department of InformaticsUniversity of BergenNorway