Generating and characterizing the perfect elimination orderings of a chordal graph

Authors:
L. S. Chandran;L. Ibarra;F. Ruskey;J. Sawada
Affiliations:
Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India;School of CTI, DePaul University, Chicago, IL and Department of Computer Science, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6;Department of Computer Science, University of Victoria, Victoria, British Columbia, Canada V8W 3P6;Department of Computer Science, University of Toronto, Toronto, Ontario, Canada and Department of Computer Science, University of Victoria, Victoria, British Columbia, Canada V8W 3P6
Venue:
Theoretical Computer Science - Random generation of combinatorial objects and bijective combinatorics
Year:
2003

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Abstract

We develop a constant time transposition "oracle" for the set of perfect elimination orderings of chordal graphs. Using this oracle, we can generate a Gray code of all perfect elimination orderings in constant amortized time using known results about antimatroids. Using clique trees, we show how the initialization of the algorithm can be performed in linear time. We also develop two new characterizations of perfect elimination orderings: one in terms of chordless paths, and the other in terms of minimal u-v separators.