Performance guarantees on a sweep-line heuristic for covering rectilinear polygons with rectangles
SIAM Journal on Discrete Mathematics
Perfect graphs and orthogonally convex covers
SIAM Journal on Discrete Mathematics
Covering orthogonal polygons with star polygons: the perfect graph approach
Journal of Computer and System Sciences
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Journal of Algorithms
Approximation algorithms for NP-hard problems
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Approximation algorithms for NP-hard problems
Approximation algorithms
Approximation Algorithms for Covering Polygons with Squares and Similar Problems
RANDOM '97 Proceedings of the International Workshop on Randomization and Approximation Techniques in Computer Science
Covering Rectilinear Polygons with Axis-Parallel Rectangles
SIAM Journal on Computing
Rectangle covers revisited computationally
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
Silhouette area based similarity measure for template matching in constant time
AMDO'10 Proceedings of the 6th international conference on Articulated motion and deformable objects
Algorithms and theory of computation handbook
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We consider the problem of covering an orthogonal polygon with a minimum number of axis-parallel rectangles from a computational point of view. We propose an integer program which is the first general approach to obtain provably optimal solutions to this well-studied NP-hard problem. It applies to common variants like covering only the corners or the boundary of the polygon and also to the weighted case. In experiments, it turns out that the linear programming relaxation is extremely tight and rounding a fractional solution is an immediate high-quality heuristic. We obtain excellent experimental results for polygons originating from VLSI design, fax data sheets, black and white images, and for random instances. Making use of the dual linear program, we propose a stronger lower bound on the optimum, namely, the cardinality of a fractional stable set. Furthermore, we outline ideas how to make use of this bound in primal--dual-based algorithms. We give partial results, which make us believe that our proposals have a strong potential to settle the main open problem in the area: To find a constant factor approximation algorithm for the rectangle cover problem.