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On the completability of incomplete orthogonal Latin rectangles

Appa, Gautam and Euler, R. and Kouvela, Anastasia and 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

Abstract

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
Official URL: http://www.elsevier.com/locate/disc
Additional Information: © 2016 Elsevier
Subjects: Q Science > QA Mathematics
Sets: Departments > Management
Date Deposited: 16 Jun 2016 09:48
Last Modified: 19 Sep 2017 14:25
Funders: Athens University of Economics and Business
URI: http://eprints.lse.ac.uk/id/eprint/66929

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