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On the completability of incomplete orthogonal Latin rectangles

Appa, Gautam, Euler, R., Kouvela, Anastasia, Magos, D. and Mourtos, I. (2016) On the completability of incomplete orthogonal Latin rectangles. Discrete Mathematics. ISSN 0012-365X

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Identification Number: 10.1016/j.disc.2016.02.008


We address the problem of completability for 2-row orthogonal Latin rectangles (OLR2). Our approach is to identify all pairs of incomplete 2-row Latin rectangles that are not com- pletable to an OLR2 and are minimal with respect to this property; i.e., we characterize all circuits of the independence system associated with OLR2. Since there can be no poly- time algorithm generating the clutter of circuits of an arbitrary independence system, our work adds to the few independence systems for which that clutter is fully described. The result has a direct polyhedral implication; it gives rise to inequalities that are valid for the polytope associated with orthogonal Latin squares and thus planar multi-dimensional assign- ment. A complexity result is also at hand: completing a set of (n - 1) incomplete MOLR2 is NP-complete.

Item Type: Article
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Additional Information: © 2016 Elsevier
Divisions: Management
Subjects: Q Science > QA Mathematics
Date Deposited: 16 Jun 2016 09:48
Last Modified: 07 Jan 2024 19:18
Funders: Athens University of Economics and Business

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