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A complete resolution of the Keller maximum clique problem

Author(s)
Debroni, Jennifer; Eblen, John D.; Langston, Michael A.; Myrvold, Wendy; Shor, Peter W.; Weerapurage, Dinesh; ... Show more Show less
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Abstract
A d-dimensional Keller graph has vertices which are numbered with each of the 4[superscript d] possible d-digit numbers (d-tuples) which have each digit equal to 0, 1, 2, or 3. Two vertices are adjacent if their labels differ in at least two positions, and in at least one position the difference in the labels is two modulo four. Keller graphs are in the benchmark set of clique problems from the DIMACS clique challenge, and they appear to be especially difficult for clique algorithms. The dimension seven case was the last remaining Keller graph for which the maximum clique order was not known. It has been claimed in order to resolve this last case it might take a "high speed computer the size of a major galaxy". This paper describes the computation we used to determine that the maximum clique order for dimension seven is 124.
Date issued
2011
URI
http://hdl.handle.net/1721.1/81184
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, SODA '11
Publisher
Association for Computing Machinery (ACM)
Citation
Jennifer Debroni, John D. Eblen, Michael A. Langston, Wendy Myrvold, Peter Shor, and Dinesh Weerapurage. 2011. A complete resolution of the Keller maximum clique problem. In Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms (SODA '11). SIAM 129-135. Copyright © SIAM 2011
Version: Final published version

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