On Completing Latin Squares

We present a (2 3 − o(1))-approximation algorithm for the partial latin square extension (PLSE) problem. This improves the current best bound of 1 − 1 e due to Gomes, Regis, and Shmoys [5]. We also show that PLSE is APX-hard. We then consider two new and natural variants of PLSE. In the first, there is an added restriction that at most k colors are to be used in the extension; for this problem, we prove a tight approximation threshold of 1 − 1 e . In the second, the goal is to find the largest partial latin square embedded in the given partial latin square that can be extended to completion; we obtain a 1 4 approximation algorithm in this case.

• Type: Conference
• Year: 2007
• Where: STACS
• Authors: Iman Hajirasouliha, Hossein Jowhari, Ravi Kumar, Ravi Sundaram
• Keywords: Latin Square Extension, Partial Latin Square, STACS 2007, Theoretical Computer Science, Tight Approximation Threshold