Filtering algorithms for the multiset ordering constraint

Filtering Algorithms for the Multiset Ordering Constraint

Article history: Received 1 July 2008 Received in revised form 17 October 2008 Accepted 2 November 2008 Available online 6 November 2008

Constraint Multiset

Multiset Ordering Constraints

We identify a new and important global (or non-binary) constraint. This constraint ensures that the values taken by two vectors of variables, when viewed as multisets, are ordered. This constraint is useful for a number of different applications including breaking symmetry and fuzzy constraint satisfaction. We propose and implement an efficient linear time algorithm for enforcing generalised ar...

Linear-Time Filtering Algorithms for the Disjunctive Constraint

We present three new filtering algorithms for the DISJUNCTIVE constraint that all have a linear running time complexity in the number of tasks. The first algorithm filters the tasks according to the rules of the time tabling. The second algorithm performs an overload check that could also be used for the CUMULATIVE constraint. The third algorithm enforces the rules of detectable precedences. Th...

Variety Reasoning for Multiset Constraint Propagation

Set variables in constraint satisfaction problems (CSPs) are typically propagated by enforcing set bounds consistency together with cardinality reasoning, which uses some inference rules involving the cardinality of a set variable to produce more prunings than set bounds propagation alone. Multiset variables are a generalization of set variables by allowing the elements to have repetitions. In ...