Forbidden-set distance labels for graphs of bounded doubling dimension

This article proposes a forbidden-set labeling scheme for the family of unweighted 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 + ϵ^-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 O(1 + ϵ)^2α · |F|² log n time, a 1 + ϵ stretch approximation for the distance between s and t in the graph G \ F. The labeling scheme can be extended into a forbidden-set labeled routing scheme with stretch 1 + ϵ for graphs of bounded doubling dimension.