Forbidden-set distance labels for graphs of bounded doubling dimension

Abstract

The paper proposes a forbidden-set labeling scheme for the family of graphs with doubling dimension bounded by α. For an n-vertex graph G in this family, and for any desired precision parameter ε > 0, the labeling scheme stores an O(1+α-1)2α log2 n-bit label at each vertex. Given the labels of two end-vertices s and t, and the labels of a set F of "forbidden" vertices and/or edges, our scheme can compute, in time polynomial in the length of the labels, a 1+ε stretch approximation for the distance between s and t in the graph GF. The labeling scheme can be extended into a forbidden-set labeled routing scheme with stretch 1 + ε for graphs of bounded doubling dimension.