Mircea Marin (West University of Timisoara, Romania) |
Temur Kutsia (Johannes Kepler University, Linz, Austria) |
Cleo Pau (Johannes Kepler University, Linz, Austria) |
Mikheil Rukhaia (Institute of Applied Mathematics, Tbilisi State University, Georgia) |
We address the problem of enumerating all maximal clique-partitions of an undirected graph and present an algorithm based on the observation that every maximal clique-partition can be produced from the maximal clique-cover of the graph by assigning the vertices shared among maximal cliques, to belong to only one clique. This simple algorithm has the following drawbacks: (1) the search space is very large; (2) it finds some clique-partitions which are not maximal; and (3) some clique-partitions are found more than once. We propose two criteria to avoid these drawbacks. The outcome is an algorithm that explores a much smaller search space and guarantees that every maximal clique-partition is computed only once. The algorithm can be used in problems such as anti-unification with proximity relations or in resource allocation tasks when one looks for several alternative ways to allocate resources. |
ArXived at: https://dx.doi.org/10.4204/EPTCS.389.6 | bibtex | |
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