Approximating Latin Square Extensions

In this paper, we consider the following question: what is the maximum number of entries that can be added to a partially lled latin square? The decision version of this question is known to be NP-complete. We present two approximation algorithms for the optimization version of this question. We rst prove that the greedy algorithm achieves a factor of 1/3. We then use insights derived from the linear relaxation of an integer program to obtain an algorithm based on matchings that achieves a better performance guarantee of 1/2. These are the rst known polynomial-time approximation algorithms for the latin square completion problem that achieve non-trivialworst-case performance guarantees. Our motivationderives fromapplications to the problems of lightpath assignment and switch con guration in wavelength routed multihop optical networks. 1 Motivation

• Type: Journal
• Year: 1999
• Where: ALGORITHMICA
• Authors: Ravi Kumar, Alexander Russell, Ravi Sundaram
• Keywords: ALGORITHMICA 1999, Approximation Algorithms, Latin Square, Performance Guarantees