Linear-time filtering algorithms for the disjunctive constraint and a quadratic filtering algorithm for the cumulative not-first not-last

Abstract

We present new filtering algorithms for Disjunctive and Cumulative constraints, each of which improves the complexity of the state-of-theart algorithms by a factor of log n. We show how to perform Time-Tabling and Detectable Precedences in linear time on the Disjunctive constraint. Furthermore, we present a linear-time Overload Checking for the Disjunctive and Cumulative constraints. Finally, we show how the rule of Not-first/Not-last can be enforced in quadratic time for the Cumulative constraint. These algorithms rely on the union find data structure, from which we take advantage to introduce a new data structure that we call it time line. This data structure provides constant time operations that were previously implemented in logarithmic time by the Θ-tree data structure. Experiments show that these new algorithms are competitive even for a small number of tasks and outperform existing algorithms as the number of tasks increases. We also show that the time line can be used to solve specific scheduling problems.

Using Approximation within Constraint Programming to Solve the Parallel Machine Scheduling Problem with Additional Unit Resources

“…In the following, we use DISJUNCTIVE constraints as described in (Fahimi, Ouellet, and Quimper 2018). For CUMULATIVE constraints, we use the edge-finding algorithm from (Vilím 2009), the time-tabling algorithm from (Ouellet and Quimper 2013) and the not-first/not-last and overload-checking algorithms from (Fahimi, Ouellet, and Quimper 2018). For all i ∈ [n], let T i be a task variable, which starts at s i lasts p i and ends at e i .…”