Not-First and not-last detection for cumulative scheduling in O(n3 log n)

Authors:
Andreas Schutt;Armin Wolf;Gunnar Schrader
Affiliations:
Fraunhofer FIRST, Germany;Fraunhofer FIRST, Germany;Fraunhofer FIRST, Germany
Venue:
INAP'05 Proceedings of the 16th international conference on Applications of Declarative Programming and Knowledge Management
Year:
2005

Citing 4
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Abstract

Not-first/not-last detection is the pendant of edge-finding in constraint-based disjunctive and cumulative scheduling. Both methods provide strong pruning algorithms in constraint programming. This paper shows that the not-first/not-last detection algorithm presented by Nuijten that runs in time ${\cal O}(n^3k)$ is incorrect and incomplete, where n is the number of tasks and k is the number of different capacity requirements of these tasks. A new correct and complete detection algorithm for cumulative scheduling is then presented which runs in ${\cal O}(n^3\log n)$.