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.
This work was supported by the National Science Foundation through the Career: Cornflower Project (award number 0644113).
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Malitsky, Y., Sellmann, M., van Hoeve, WJ. (2008). Length-Lex Bounds Consistency for Knapsack Constraints. In: Stuckey, P.J. (eds) Principles and Practice of Constraint Programming. CP 2008. Lecture Notes in Computer Science, vol 5202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85958-1_18
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DOI: https://doi.org/10.1007/978-3-540-85958-1_18
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