Recognizing integrality of weighted rectangles partitions

Paul Deuker () and Ulf Friedrich ()
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Paul Deuker: Tilburg University
Ulf Friedrich: Otto von Guericke University Magdeburg

Journal of Combinatorial Optimization, 2025, vol. 49, issue 2, No 2, 15 pages

Abstract: Abstract Given a grid of active and inactive pixels, the weighted rectangles partitioning (WRP) problem is to find a maximum-weight partition of the active pixels into rectangles. WRP is formulated as an integer programming problem and instances with an integral relaxation polyhedron are characterized by a balanced problem matrix. A complete characterization of these balanced instances is proved. In addition, computational results on balancedness recognition and on solving WRP are presented.

Keywords: Partition problem; Rectangles; Integer programming; Balanced matrix; 90C10; 90C05; 05C50 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-024-01252-5

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