A 116/13-approximation algorithm for l(2, 1)-labeling of unit disk graphs

Abstract

Given a graph, an L(2, 1)-labeling of the graph is an assignment l from the vertex set to the set of nonnegative integers such that for any pair of vertices (u, v), (formula Presented) if u and v are adjacent, and (formula Presented) if u and v are at distance 2. The L(2, 1)-labeling problem is to minimize the span of l (i.e., (formula Presented)). In this paper, we propose a new polynomial-time 116/13-approximation algorithm for L(2, 1)-labeling of unit disk graphs. This improves the previously best known ratio 12.