A quasi-polynomial time approximation scheme for minimum weight triangulation

  • Authors:
  • Jan Remy;Angelika Steger

  • Affiliations:
  • ETH Zürich, Zürich, Switzerland;ETH Zürich, Zürich, Switzerland

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 2009

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Abstract

The Minimum Weight Triangulation problem is to find a triangulation T* of minimum length for a given set of points P in the Euclidean plane. It was one of the few longstanding open problems from the famous list of twelve problems with unknown complexity status, published by Garey and Johnson [1979]. Very recently, the problem was shown to be NP-hard by Mulzer and Rote [2006]. In this article, we present a quasi-polynomial time approximation scheme for Minimum Weight Triangulation.