Length-Lex Bounds Consistency for Knapsack Constraints

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 domainstore 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.