Consecutive Ones Matrices for Multi-dimensional Orthogonal Packing Problems
The multi-dimensional orthogonal packing problem (OPP) is a well studied decisional problem. Given a set of items with rectangular shapes, the problem is to decide whether there is a non-overlapping packing of these items in a rectangular bin. The rotation of items is not allowed. A powerful caracterization of packing configurations by means of interval graphs was recently introduced. In this paper, we propose a new algorithm using consecutive ones matrices as data structure. This new algorithm is then used to solve the two-dimensional orthogonal knapsack problem. Computational results are reported, which show its effectiveness.
KeywordsOrthogonal packing problem Interval graph Consecutive ones matrices
Unable to display preview. Download preview PDF.
- 4.Beasley, J.E., Mingozzi, A.: A New Formulation for the two-dimensional Orthogonal Cutting Problem. Tech. rep., University of Bologna, Italy (1996)Google Scholar
- 5.Beldiceanu, N., Carlsson, M.: New filtering for the cumulative constraint in the context of non-overlapping rectangles. In: Lecture Notes in Computer Science, CPAIOR08, vol. 5015, pp. 21–25 (2008)Google Scholar
- 7.Below, G., Scheithauer, G.: Lower-dimensional bounds and a new model for higher-dimensional orthogonal packing (2008)Google Scholar
- 20.Ferreira, E., Oliveira, J.: Fekete and Schepers’ Graph-based Algorithm for the Two-Dimensional Orthogonal Packing Problem Revisited. Gabler (2008)Google Scholar
- 21.Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of np-completeness (1979)Google Scholar
- 23.Onodera, H., Taniguchi, Y., Tamaru, K.: Branch-and-bound placement for building block layout. In: 28th ACM/IEEE Design Automation Conference, pp. 433–439 (1991)Google Scholar
- 26.Simonis, H., O’Sullivan, B.: Search Strategies for Rectangle Packing (2008)Google Scholar