A new algorithm for the Orthogonal Packing Problem
Petru Valicov
25 May 2012, 15h00 - 25 May 2012, 16h00 Salle/Bat : 445/PCRI-N
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Résumé :
Let $V$ be a set of rectangular items and $C$ a rectangular container. The two-dimensional Orthogonal Packing Problem (OPP-2) consists in deciding whether the set $V$ can be packed in $C$ without overlapping and without rotating the items. If the set $V$ can be packed in $C$, then $V$ is called a feasible set. This problem is NP-complete and can be seen as a sub-problem of the well known two-dimensional Orthogonal Knapsack Problem. Fekete and Schepers introduced a powerful characterization of feasible packings, based on interval graphs. Using this characterization they designed an efficient algorithm to solve OPP by enumerating the interval graphs with a certain number of constraints. In this work, we present a new algorithm for solving OPP-2 based on a more compact representation of interval graphs. One of the main advantages is having a reduced number of "symmetrical" solutions. This is a joint work with C. Joncour and A. Pêcher.
