Abstract
We study the “inter-distance constraint,” also known as the global minimum distance constraint, that ensures that the distance between any pair of variables is at least equal to a given value. When this value is 1, the inter-distance constraint reduces to the all-different constraint. We introduce an algorithm to propagate this constraint and we show that, when variables domains are intervals, our algorithm achieves arc-B-consistency. It provides tighter bounds than generic scheduling constraint propagation algorithms (like edge-finding) that could be used to capture this constraint. The worst case complexity of the algorithm is cubic but it behaves well in practice and it drastically reduces the search space. Experiments on special Job-Shop problems and on an Air-Traffic problem known as the “Runway Sequencing” problem.
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Artiouchine, K., Baptiste, P. Arc-B-consistency of the Inter-distance Constraint. Constraints 12, 3–19 (2007). https://doi.org/10.1007/s10601-006-9009-1
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DOI: https://doi.org/10.1007/s10601-006-9009-1