Léon Planken

Kim van den Houten, Léon Planken, Esteban Freydell et al.

This study investigates scheduling strategies for the stochastic resource-constrained project scheduling problem with maximal time lags (SRCPSP/max)). Recent advances in Constraint Programming (CP) and Temporal Networks have reinvoked interest in evaluating the advantages and drawbacks of various proactive and reactive scheduling methods. First, we present a new, CP-based fully proactive method. Second, we show how a reactive approach can be constructed using an online rescheduling procedure. A third contribution is based on partial order schedules and uses Simple Temporal Networks with Uncertainty (STNUs). Our statistical analysis shows that the STNU-based algorithm performs best in terms of solution quality, while also showing good relative offline and online computation time.

Léon R. Planken, Mathijs M. de Weerdt, Roman P. J. van der Krogt

We present two new and efficient algorithms for computing all-pairs shortest paths. The algorithms operate on directed graphs with real (possibly negative) weights. They make use of directed path consistency along a vertex ordering d. Both algorithms run in O(n^2 w_d) time, where w_d is the graph width induced by this vertex ordering. For graphs of constant treewidth, this yields O(n^2) time, which is optimal. On chordal graphs, the algorithms run in O(nm) time. In addition, we present a variant that exploits graph separators to arrive at a run time of O(n w_d^2 + n^2 s_d) on general graphs, where s_d andlt= w_d is the size of the largest minimal separator induced by the vertex ordering d. We show empirically that on both constructed and realistic benchmarks, in many cases the algorithms outperform Floyd-Warshalls as well as Johnsons algorithm, which represent the current state of the art with a run time of O(n^3) and O(nm + n^2 log n), respectively. Our algorithms can be used for spatial and temporal reasoning, such as for the Simple Temporal Problem, which underlines their relevance to the planning and scheduling community.