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Abstract: We consider the following problem, called Relative Minimal Elimination Ordering. Given a graph G = (V; E) which is a subgraph of the chordal graph G 0 = (V; E 0 ), compute an inclusion minimal chordal graph G 00 = (V; E 00 ), such that E ` E 00 ` E 0 . We show that this can be done in O(nm) time. This extends the results of [2]. The algorithm is based only on well known results on chordal graphs. 1 Introduction One of the major problems in computational linear algebra is that... (Update)
Context of citations to this paper: More
.... heuristic in order to improve it yet further, although recent research has been done on algorithms for low ll minimal triangulations [5, 7, 23]. In this paper, we use recent graph theoretical results on minimal triangulation and minimal separation to explain, at least in part,...
...such that no subgraph of H is a triangulation of G. Several practical algorithms exist for finding minimal triangulations [1] 2] [3], 5] 8] 9] One such classical algorithm, called Lex M [9] is derived from the Lex BFS (lexicographic breadth first search) algorithm...
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10: Algorithmic aspects of vertex elimination on graphs (context) - Rose, Tarjan et al. - 1976
7: Computing the minimum fill-in is NP-complete (context) - Yannakakis - 1981
6: The intersection graphs of subtrees in trees are exactly the chordal graphs (context) - Gavril - 1974
BibTeX entry: (Update)
E. Dahlhaus. Minimal elimination ordering inside a given chordal graph. In Graph Theoretical Concepts in Computer Science, pages 132--143. Springer Verlag, 1997. Lecture Notes in Computer Science 1335. http://citeseer.ist.psu.edu/dahlhaus99minimal.html More
@incollection{ dahlhausdahlhausminimal,
author = "E. Dahlhaus",
title = "Minimal Elimination Ordering Inside a Given Chordal Graph",
booktitle = "Graph-theoretic concepts in computer science, Proc. of the 23rd international workshop, {WG} '97, (Berlin, 1997)",
volume = "1335",
publisher = "Springer-Verlag",
editor = "R. H. Moehring",
pages = "132--143",
url = "citeseer.ist.psu.edu/dahlhaus99minimal.html" }
Citations (may not include all citations):346 Computer Solution of Large Sparse Positive Definite Systems (context) - George, Liu - 1981
178 Algorithmic Aspects on Vertex Elimination on Graphs (context) - Rose, Tarjan et al. - 1976
93 Computing the Minimum Fill-in is NP-complete (context) - Yannakakis - 1981
78 Efficiency of a Good but not Linear Set Union Algorithm (context) - Tarjan - 1975
77 Parallel Connectivity Algorithm (context) - Shiloach, Vishkin et al. - 1982
73 Triangulated Graphs and the Elimination Process (context) - Rose - 1970
53 The Intersection Graphs of Subtrees in Trees Are Exactly the.. (context) - Gavril - 1974
34 Characterizations of Strongly Chordal Graphs (context) - Farber - 1983
11 Minimal Elimination Ordering inside a Given Chordal Graph - Dahlhaus - 1997
10 An Efficient Parallel Algorithm for the Minimal Elimination .. - Dahlhaus, Karpinski - 1994
8 A Characterization of Rigid Circuit Graphs (context) - Bunemann - 1974
7 Parallel Solution of Sparse Linear Systems (context) - Gilbert, Hafsteinsson - 1988
6 Cutting Down on Fill-in Using Nested Dissection (context) - Agrawal, Klein et al. - 1993
6 Making an Arbitrary Filled Graph Minimal by Removing Fill Ed.. - Blair, Heggernes et al.
6 How to use minimal separators for its chordal triangulation (context) - Parra, Scheffler - 1995
5 Fast parallel algorithm for the single link heuristics of hi.. (context) - Dahlhaus - 1992
2 Sequential and Parallel Algorithms on Compactly Represented .. (context) - Dahlhaus - 1997
2 Efficient Parallel Algorithms on Chordal Graphs with a Spars.. - Dahlhaus - 1994
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