Length-lex bounds consistency for knapsack constraints

Abstract

Recently, a new domain store for set-variables has been proposed which totally orders all values in the domain of a set-variable based on cardinality and lexicography. Traditionally, knapsack constraints have been studied with respect to the required and possible set domain representation. For this domain-store efficient filtering algorithms achieving relaxed and approximated consistency are known. In this work, we study the complexity of achieving length-lex and approximated length-lex bounds consistency. We show that these strengthened levels of consistency can still be achieved in (pseudo-)polynomial time. In addition, we devise heuristic algorithms that work efficiently in practice. © 2008 Springer-Verlag Berlin Heidelberg.