A Whirling Dervish: Polynomial-Time Algorithm for the Regional SRLG-Disjoint Paths Problem

• Published in: IEEE/ACM transactions on networking Vol. 31; no. 6; pp. 1 - 12
• Main Authors: Vass, Balazs, Berczi-Kovacs, Erika R., Barabas, Abel, Hajdu, Zsombor Laszlo, Tapolcai, Janos
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Best practice; disaster resilience; Faces; Failure; Graph theory; IEEE transactions; Minimax techniques; Network topologies; Network topology; Planning; polynomial algorithm; Polynomials; Routing; shared risk link group (SRLG); Shortest-path problems; Topology
• ISSN: 1063-6692; 1558-2566
• DOI: 10.1109/TNET.2023.3276815

The current best practice in survivable routing is to compute link or node disjoint paths in the network topology graph. It can protect single-point failures; however, several failure events may cause the interruption of multiple network elements. The set of network elements subject to potential failure events is called Shared Risk Link Group (SRLG), identified during network planning. Unfortunately, for any given list of SRLGs, finding two paths that can survive a single SRLG failure is NP-Complete. In this paper, we provide a polynomial-time SRLG-disjoint routing algorithm for planar network topologies and a large set of SRLGs. Namely, we focus on regional failures, where the failed network elements must not be far from each other. We use a flexible definition of regional failure, where the only restrictions are that i) the topology is a planar graph, ii) each SRLG forms a set of connected edges in the dual of the planar graph, and iii) for each node <inline-formula> <tex-math notation="LaTeX">v</tex-math> </inline-formula>, the links incident to <inline-formula> <tex-math notation="LaTeX">v</tex-math> </inline-formula> are part of an SRLG. The proposed algorithm is based on a max-min theorem. Through extensive simulations, we show that the algorithm scales well with the network size, and one of the paths returned by the algorithm is only <inline-formula> <tex-math notation="LaTeX">4</tex-math> </inline-formula>% longer than the shortest path on average.