Strong Conflict-Free Coloring with Respect to Intervals and Circular Intervals

Given a hypergraph H = (V, E), a coloring of its vertices is said to be conflict-free if for every hyperedge S ∈ E there is at least one vertex in S whose color is distinct from the colors of all other vertices in S. More generally if every hyperedge has k-distinct color then the coloring is called k-strong conflict-free coloring. In this paper, we present a polynomial k-strong conflict-free coloring algorithm for set of discrete intervals (referred as hyperedge denoted by Hn) and also present a polynomial algorithm for a special case where we take only some of the subsets of Hn such that each subset have at least k unique color. Our algorithm uses at most 2k(logn 2 )+ 1 color in