Improved Local Algorithms for Spanner Construction

Abstract

Let S be a set of n points in the plane, let e be the complete Euclidean graph whose point-set is S, and let G be the Delaunay triangulation of S. We present a very simple local algorithm that, given G, constructs a subgraph of G of degree at most 11 that is a geometric spanner of G with stretch factor 2.86, and hence a geometric spanner of e with stretch factor < 7. This algorithm gives an O(n lg n) time centralized algorithm for constructing a subgraph of G that is a geometric spanner of e of degree at most 11 and stretch factor < 7. The algorithm can be generalized to unit disk graphs to give a local algorithm for constructing a plane spanner of a unit disk graph of degree at most 11 and stretch factor < 7.