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 \({\cal O}(n^3\log n)\).
The work presented in this paper is partly funded by the European Union (EFRE) and the state Berlin within the research project “inubit MRP”, grant no. 10023515.
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Schutt, A., Wolf, A., Schrader, G. (2006). Not-First and Not-Last Detection for Cumulative Scheduling in \({\cal O}(n^3\log n)\) . In: Umeda, M., Wolf, A., Bartenstein, O., Geske, U., Seipel, D., Takata, O. (eds) Declarative Programming for Knowledge Management. INAP 2005. Lecture Notes in Computer Science(), vol 4369. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11963578_6
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DOI: https://doi.org/10.1007/11963578_6
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