Enumeration of Circuits and Minimal Forbidden Sets

F. Stork, M.J. Uetz

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In resource-constrained scheduling, it is sometimes important to know all inclusion-minimal subsets of jobs that must not be scheduled simultaneously. These so-called minimal forbidden sets are given implicitly by a linear inequality system, and can be interpreted more generally as the circuits of a particular independence system. We present several complexity results related to computation, enumeration, and counting of the circuits of an independence system. On this account, we also propose a backtracking algorithm that enumerates all minimal forbidden sets for resource constrained scheduling problems.
Original languageEnglish
Pages (from-to)112-115
JournalElectronic Notes in Discrete Mathematics
Publication statusPublished - 1 Jan 2003


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