Computation Initial Degree and Waldschmidt Constant for Sets of Small Number of Multiple Points

Abstract

Waldschmidt constant is firstly introduced by Waldschmidt in 1975. Since then, many results of this constant was achieved mostly about finding lower bounds. That is recently one of active, fascinating and important topics. However, computation of Waldschmidt constant or the initial degree is very hard in general, even for cases of small numbers of points  in the projective plane. Recently, the constants were computed for certain sets of points with one, two and three supporting lines. The paper shows values of the initial degree and Waldschmidt constant for sets with at most 6 points in all configurations in projective plane. These constants represent the complexity of optimal solutions in repeated path problems that have many applications in computer science, informatics theory and telecommunications.