Resilient arcs and node disjointness in diverse routing

Abstract

In multi-layer networks protection can be provided at multiple layers. Hence some links at an upper layer may be {\it resilient} because they are protected at a lower layer. We will designate as {\it resilient arc} at a given layer, an arc which has some form of protection at an underlaying layer. When path diversity is used at an upper layer, and resilient arcs are taken into account, it may not be necessary for the considered paths to be fully disjoint. We solve a problem of finding the shortest node-disjoint pair of paths that can share resilient arcs. It is assumed that a network consists of a set of nodes and a set of arcs. Moreover, a number of available arcs are resilient. Our goal is to find the shortest pair of paths such that they share only those nodes that are incident to shared resilient arcs. Moreover, we assume that the resulting paths cannot contain loops, and costs of shared resilient arcs are counted only once towards the objective function. In the paper we present two novel algorithms solving the above problem, and two supporting algorithms that are utilized as subroutines. We implement the proposed algorithms and compare them to an MIP approach.