Fault-Tolerant Edge-Disjoint Paths -- Beyond Uniform Faults

TL;DR

This paper explores fault-tolerant network design beyond uniform failure models, focusing on path and flow problems with refined fault scenarios, and provides complexity results and algorithms highlighting increased difficulty.

Contribution

It introduces and analyzes the Fault-Tolerant Path and Flow problems under a refined fault model, extending beyond traditional uniform assumptions, with new complexity insights and algorithms.

Findings

Complexity increases significantly compared to uniform fault models.

Exact and approximation algorithms are developed for the new fault-tolerant problems.

The problems are shown to be more challenging than classical edge-disjoint paths.

Abstract

The overwhelming majority of survivable (fault-tolerant) network design models assume a uniform fault model. Such a model assumes that every subset of the network resources (edges or vertices) of a given cardinality $k$ may fail. While this approach yields problems with clean combinatorial structure and good algorithms, it often fails to capture the true nature of the scenario set coming from applications. One natural refinement of the uniform model is obtained by partitioning the set of resources into vulnerable and safe resources. The scenario set contains every subset of at most $k$ faulty resources. This work studies the Fault-Tolerant Path (FTP) problem, the counterpart of the Shortest Path problem in this fault model and the Fault-Tolerant Flow problem (FTF), the counterpart of the $\ell$-disjoint Shortest $s$-$t$ Path problem. We present complexity results alongside exact and approximation algorithms for both models. We emphasize the vast increase in the complexity of the problem with respect to the uniform analogue, the Edge-Disjoint Paths problem.