Finding minimum height elimination trees for interval graphs in polynomial time Article Received: 15 May 1993 Revised: 15 May 1994 DOI:
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 05C50 65F50 65Y05 Key words Sparse matrix computation elimination trees parallel computing interval graphs
This work was supported by grants from the Norwegian Research Council.
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