A complete resolution of the Keller maximum clique problem
Name
Shor_A complete resolution.pdf
Size
780.86 KB
Format
Adobe PDF
Checksum (MD5)
2ab9bf3395b503838639c7b02b1eab6e
Author(s)
Debroni, Jennifer
Eblen, John D.
Langston, Michael A.
Myrvold, Wendy
Shor, Peter W.
Weerapurage, Dinesh
Date Issued
2011
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
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
http://dl.acm.org/citation.cfm?id=2133047
