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Recognizing integrality of weighted rectangles partitions

Author

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  • Paul Deuker

    (Tilburg University)

  • Ulf Friedrich

    (Otto von Guericke University Magdeburg)

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.

Suggested Citation

  • Paul Deuker & Ulf Friedrich, 2025. "Recognizing integrality of weighted rectangles partitions," Journal of Combinatorial Optimization, Springer, vol. 49(2), pages 1-15, March.
    • Handle: RePEc:spr:jcomop:v:49:y:2025:i:2:d:10.1007_s10878-024-01252-5
    DOI: 10.1007/s10878-024-01252-5
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    References listed on IDEAS

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