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

PDF - Accepted Version
Restricted to Repository staff only until 11 March 2017.
Download (602Kb)

LSE expert's profile

Published item via DOI

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:

Library of Congress subject classification:

Q Science > QA Mathematics

Sets:

Departments > Management

Project and Funder Information: