An 8-approximation algorithm for L(2,1)-labeling of unit disk graphs

Given a graph G=(V,E), 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), |ℓ(u)−ℓ(v)|≥2 if u and v are adjacent, and ℓ(u)≠ℓ(v) if u and v are at distance 2. The L(2,1)-labeling problem is to minimize the range of ℓ (i.e., maxu∈V(ℓ(u))−minu∈V(ℓ(u))+1). Although the problem is generally hard to approximate within any constant factor, it was known to be approximable within factor 10.67 for unit disk graphs. This paper designs a new way of partitioning the plane into squares for periodic labeling, based on which we present an 8-approximation polynomial-time algorithm for L(2,1)-labeling of unit disk graphs.