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 \(\ell \) from the vertex set to the set of nonnegative integers such that for any pair of vertices (u, v), \(|\ell (u) - \ell (v)| \ge 2\) if u and v are adjacent, and \(\ell (u) \ne \ell (v)\) if u and v are at distance 2. The L(2, 1)-labeling problem is to minimize the span of \(\ell \) (i.e., \(\max _{u \in V}(\ell (u)) - \min _{u \in V}(\ell (u)) + 1\)). 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.