Improved Runtimes and Lower Bounds for Dual-Edge Failure Replacement Path Algorithms

Abstract

Given a graph G and a fixed pair of nodes s and t, the Replacement Paths problem is to compute the new shortest distance from s to t when there are edge failures in G (i.e. those edges can no longer be used for any path). While there has been extensive research into the single-failure Replacement Paths problem, less progress has been made on multiple-failure algorithms. This thesis provides a new algorithm for the two-failure variant of the Replacement Paths problem, and shows a new combinatorial lower bound for the runtime of k-failure Replacement Paths for any positive integer k.