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On Completing Latin Squares

  • Iman Hajirasouliha
  • Hossein Jowhari
  • Ravi Kumar
  • Ravi Sundaram
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)

Abstract

We present a \((\frac{2}{3}-\epsilon)\)-approximation algorithm for the partial latin square extension (PLSE) problem. This improves the current best bound of \(1 - \frac{1}{e}\) 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 \(1-\frac{1}{e}\). 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 \(\frac{1}{4}\)-approximation algorithm in this case.

Keywords

Approximation Algorithm Greedy Algorithm Empty Cell Extension Problem Polynomial Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Iman Hajirasouliha
    • 1
  • Hossein Jowhari
    • 1
  • Ravi Kumar
    • 2
  • Ravi Sundaram
    • 3
  1. 1.Simon Fraser University, Burnaby, BC, V5A 1S6Canada
  2. 2.Yahoo! Research, Sunnyvale, CA 94089USA
  3. 3.Northeastern University, Boston, MA 02115USA

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