Shortest Paths Avoiding Forbidden Subpaths

TL;DR

This paper introduces an algorithm for finding shortest paths in graphs that avoid certain forbidden subpaths, with applications in optical networks, even when the set of forbidden paths is initially unknown.

Contribution

It proposes a novel algorithm that discovers and avoids forbidden subpaths dynamically during shortest path computation, without prior knowledge of these paths.

Findings

Algorithm finds shortest exception-avoiding paths in polynomial time.

The method dynamically detects forbidden subpaths during search.

Applicable to optical networks and similar scenarios.

Abstract

In this paper we study a variant of the shortest path problem in graphs: given a weighted graph G and vertices s and t, and given a set X of forbidden paths in G, find a shortest s-t path P such that no path in X is a subpath of P. Path P is allowed to repeat vertices and edges. We call each path in X an exception, and our desired path a shortest exception-avoiding path. We formulate a new version of the problem where the algorithm has no a priori knowledge of X, and finds out about an exception x in X only when a path containing x fails. This situation arises in computing shortest paths in optical networks. We give an algorithm that finds a shortest exception avoiding path in time polynomial in |G| and |X|. The main idea is to run Dijkstra's algorithm incrementally after replicating vertices when an exception is discovered.