On Searching Multiple Disjoint Shortest Paths in Scale-Free Networks With Hyperbolic Geometry

Abstract

Intensive research efforts have been devoted to the study of multiple disjoint shortest paths (MDSP) in complex networks. Most existing studies on this subject, unfortunately, either require global topology information about the network to find multiple shortest paths, or merely aim at finding a single unconstrained shortest path, leaving the (constrained) MDSP on local topology much less-investigated. In this paper, we model and analyze the problem of MDSP per hyperbolic random graphs. We find that the locations of MDSP have a high probability to be close to the corresponding hyperbolic geodesics. On the basis of this observation, we identify the network navigation skeleton for the source-destination pair, and subsequently devise an algorithm for searching MDSP on such a skeleton (local topology information) in a hyperbolic space. Our experiments on both synthetic and real-world networks demonstrate that the proposed algorithm not only guarantees the success of MDSP searching, but also achieves significant gains in terms of running time.