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The 2D Subarray Polytope.
- Source :
- ENTCS: Electronic Notes in Theoretical Computer Science; Aug2019, Vol. 346, p557-566, 10p
- Publication Year :
- 2019
-
Abstract
- Given a d -dimensional array, the maximum subarray problem consists in finding an axis-parallel slice of the array maximizing the sum of its entries. In this work we start a polyhedral study of a natural integer programming formulation for this problem when d = 2. Such an exploration is motivated by the need of solving large-scale instances of the rectilinear picture compression problem (RPC), a problem which arises in different scenarios. The obtained results can be useful to solve the column generation phase of a branch and price approach for RPC, a technique that applies naturally to this problem. We thus define the 2D subarray polytope , explore conditions ensuring the validity of linear inequalities, and provide several families of facet-inducing inequalities. [ABSTRACT FROM AUTHOR]
- Subjects :
- INTEGER programming
POLYTOPES
VALIDITY of statistics
Subjects
Details
- Language :
- English
- ISSN :
- 15710661
- Volume :
- 346
- Database :
- Supplemental Index
- Journal :
- ENTCS: Electronic Notes in Theoretical Computer Science
- Publication Type :
- Periodical
- Accession number :
- 138889356
- Full Text :
- https://doi.org/10.1016/j.entcs.2019.08.049