Testing Euclidean minimum spanning trees in the plane

  • Authors:

  • Artur Czumaj;Christian Sohler

  • Affiliations:

  • University of Warwick, Coventry, UK;University of Paderborn, Bonn, Germany

  • Venue:
  • ACM Transactions on Algorithms (TALG)
  • Year:
  • 2008

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Abstract

Given a Euclidean graph G over a set P of n points in the plane, we are interested in verifying whether G is a Euclidean minimum spanning tree (EMST) of P or G differs from it in more than ε n edges. We assume that G is given in adjacency list representation and the point/vertex set P is given in an array. We present a property testing algorithm that accepts graph G if it is an EMST of P and that rejects with probability at least 2/3 if G differs from every EMST of P in more than ε, n edges. Our algorithm runs in O(&sqrt;n/ε ⋅ log2 (n/ε)) time and has a query complexity of O(&sqrt;n/ε ⋅ log (n/ε)).