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New Filtering for the Cumulative Constraint in the Context of Non-Overlapping Rectangles
RISE, Swedish ICT, SICS, Computer Systems Laboratory.ORCID iD: 0000-0003-3079-8095
2011 (English)In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 1, p. 27-50Article in journal (Refereed) Published
Abstract [en]

This article describes new filtering methods for the Cumulative constraint. The first method introduces bounds for the so called longest cumulative hole problem and shows how to use these bounds in the context of the Non-Overlapping constraint. The second method introduces balancing knapsack constraints which relate the total height of the tasks that end at a specific time-point with the total height of the tasks that start at the same time-point. Experiments on tight rectangle packing problems show that these methods drastically reduce both the time and the number of backtracks for finding all solutions as well as for finding the first solution. For example, we found without backtracking all solutions to 65 perfect square instances of order 22-25 and sizes ranging from 192x192 to 661x661.

Place, publisher, year, edition, pages
Springer-Verlag , 2011, 5. Vol. 1, p. 27-50
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Computer and Information Sciences
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URN: urn:nbn:se:ri:diva-23674DOI: 10.1007/s10479-010-0731-0OAI: oai:DiVA.org:ri-23674DiVA, id: diva2:1042751
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NET-WMSAvailable from: 2016-10-31 Created: 2016-10-31 Last updated: 2018-08-24Bibliographically approved

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Carlsson, Mats

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