Optimal Hub Labeling is NP-complete
Abstract
Distance labeling is a preprocessing technique introduced by Peleg [Journal of Graph Theory, 33(3)] to speed up distance queries in large networks. Herein, each vertex receives a (short) label and, the distance between two vertices can be inferred from their two labels. One such preprocessing problem occurs in the hub labeling algorithm [Abraham et al., SODA'10]: the label of a vertex v is a set of vertices x (the "hubs") with their distance d(x,v) to v and the distance between any two vertices u and v is the sum of their distances to a common hub. The problem of assigning as few such hubs as possible was conjectured to be NP-hard, but no proof was known to date. We give a reduction from the well-known Vertex Cover problem on graphs to prove that finding an optimal hub labeling is indeed NP-hard.
Cite
@article{arxiv.1407.8373,
title = {Optimal Hub Labeling is NP-complete},
author = {Mathias Weller},
journal= {arXiv preprint arXiv:1407.8373},
year = {2014}
}