Finding minimum height elimination trees for interval graphs in polynomial time
 Bengt Aspvall,
 Pinar Heggernes
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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 NPhard, 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 polynomialtime algorithm for finding minimum height elimination trees for interval graphs.
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 Title
 Finding minimum height elimination trees for interval graphs in polynomial time
 Journal

BIT Numerical Mathematics
Volume 34, Issue 4 , pp 484509
 Cover Date
 19941201
 DOI
 10.1007/BF01934264
 Print ISSN
 00063835
 Online ISSN
 15729125
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 05C50
 65F50
 65Y05
 Sparse matrix computation
 elimination trees
 parallel computing
 interval graphs
 Industry Sectors
 Authors

 Bengt Aspvall ^{(1)}
 Pinar Heggernes ^{(1)}
 Author Affiliations

 1. Department of Informatics, University of Bergen, N5020, Norway