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Author Ennis, John M. ♦ Fayle, Charles M. ♦ Ennis, Daniel M.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2012
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Computer programming, programs & data
Subject Keyword Clique cover ♦ Applied statistics ♦ Letter displays
Abstract The search for minimum clique coverings of graphs appears in many practical guises and with several possible minimization goals. One reasonable goal is to minimize the number of overall cliques in a covering, while a second less well-studied but equally reasonable goal is to minimize the number of individual assignments of vertices to cliques. Both goals constitute NP-hard problems and as such require competitive algorithms for practical progress to be made toward their resolutions. In this article, we introduce a technique for accomplishing the latter goal, using a combination of data reduction and a backtracking algorithm. In addition, we demonstrate that it is not always possible to minimize both the number of cliques and the number of individual vertex-clique assignments simultaneously. This demonstration resolves an open question and underscores the need for techniques that specifically minimize the number of assignments of vertices to cliques. We then illustrate our approach in two practical examples. We follow these examples with a simulation-based comparison of our exact approach with a heuristic based on the state-of-the-art algorithm for minimizing the number of cliques in a clique covering. For this comparison, we consider graphs likely to arise in applied statistics, a category of applications for which minimizing individual vertex-clique assignments is of particular interest.
ISSN 10846654
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2012-07-01
Publisher Place New York
e-ISSN 10846654
Journal Journal of Experimental Algorithmics (JEA)
Volume Number 17
Page Count 17
Starting Page 1.1
Ending Page 1.17

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Source: ACM Digital Library