Abstract
The recent success of the lazy clause generator (a hybrid of a FD and a SAT solver) on resource-constrained project scheduling problems (RCPSP) shows the importance of the global cumulative constraint to tackle these problems. A key for an efficient cumulative propagator is a fast and correct pruning of time-bounds. The not-first/not-last rule (which is not subsumed by other rules) detects activities that cannot be run at first/last regarding to an activity set and prunes their time bounds. This paper presents a new sound not-first/not-last pruning algorithm which runs in \({\mathcal O}(n^2\log n)\), where n is the number of activities. It may not find the best adjustments in the first run, but after at most n iterations. This approach of iteration fits the setup of constraint propagation quite naturally offering the opportunity that a fixed point is reached more efficiently. Moreover, it uses a novel approach of generation of some “artificial” activities in the context of triggering pruning rules correctly. In experiments on RCPSP amongst others from the well-established PSPLib we show that the algorithm runs negligible more often than a complete algorithm while taking its advantage from the lower – to the best of our knowledge the lowest known – runtime complexity.
This work was partly funded by the European Union (EFRE) and the state Berlin, grant no. 10023515 and by the German Federal Ministry of Education and Research (BMBF), grant no. 13N10598. The core of the published results is already presented in the master thesis of Schutt [11].
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Schutt, A., Wolf, A. (2010). A New \({\mathcal O}(n^2\log n)\) Not-First/Not-Last Pruning Algorithm for Cumulative Resource Constraints. In: Cohen, D. (eds) Principles and Practice of Constraint Programming – CP 2010. CP 2010. Lecture Notes in Computer Science, vol 6308. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15396-9_36
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