Testing Euclidean minimum spanning trees in the plane

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 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 n edges. Our algorithm runs in O( n/

• Type: Journal
• Year: 2008
• Where: TALG
• Authors: Artur Czumaj, Christian Sohler
• Keywords: EMST, Euclidean Graph, Euclidean Minimum, TALG 2008