Generating and Characterizing the Perfect Elimination Orderings of a Chordal Graph. Chandran, L., Ibarra, L., Ruskey, F., & Sawada, J. Theoretical Computer Science, 307(2):303--317, October, 2003.
Paper doi abstract bibtex 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.
@article{ Chandran2003,
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.},
author = {Chandran, L.S. and Ibarra, L. and Ruskey, F. and Sawada, J.},
doi = {10.1016/S0304-3975(03)00221-4},
file = {:Users/KunihiroWASA/Dropbox/paper/2003/Chandran et al., Generating and Characterizing the Perfect Elimination Orderings of a Chordal Graph, 2003.pdf:pdf},
issn = {03043975},
journal = {Theoretical Computer Science},
keywords = {2-Processor scheduling,Antimatroid,Chordal graph,Clique tree,Gray code,Perfect elimination ordering},
month = {October},
number = {2},
pages = {303--317},
title = {{Generating and Characterizing the Perfect Elimination Orderings of a Chordal Graph}},
url = {http://www.sciencedirect.com/science/article/pii/S0304397503002214 http://linkinghub.elsevier.com/retrieve/pii/S0304397503002214},
volume = {307},
year = {2003}
}
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