An algorithm of polynomial order for computing the covering dimension of a finite space

Abstract

Finite topological spaces and the notion of dimension play an important role in digital spaces, computer graphics, image synthesis and image analysis (see, Herman, 1998 [9]; Khalimsky et al., 1990 [10]; Rosenfeld, 1979 [15]). In Georgiou and Megaritis (2011) [7] we gave an algorithm for computing the covering dimension of a finite space X using the notion of the incidence matrix of X. This algorithm has exponential order. In this paper we give a new algorithm of polynomial order for computing the covering dimension of a finite space.