Modern heuristic techniques for combinatorial problems
Modern heuristic techniques for combinatorial problems
Improved approximation algorithms for rectangle tiling and packing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
Covering Rectilinear Polygons with Axis-Parallel Rectangles
SIAM Journal on Computing
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Rectangle covers revisited computationally
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
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Geometric covering problems are found in application domains such as sensor coverage and repairing of materials. This paper considers covering problems in which a target shape to be covered is specified and a set of covering shapes is supplied. The goal is to find translational positions of the covering shapes that allow them to collectively cover the target. All the shapes are orthotopes (convex boxes). The approach provides the best known results for translational, two-dimensional orthotope covering and the first results in three and four dimensions. Experiments suggest why the strategy succeeds in certain regions of the problem domain in spite of the NP-hardness of translational orthotope covering. This leads to a novel, dimension-independent measure that significantly improves the speed of the method. Orthotopes can form enclosures for nonconvex shapes, so progress for orthotope covering is beneficial in a more general context.