How to swap a failing edge of a single source shortest paths tree

Authors:
Enrico Nardelli;Guido Proietti;Peter Widmayer
Affiliations:
Dipartimento di Matematica Pura ed Applicata, Università di L'Aquila, L'Aquila, Italy and Ist. di Analisi dei Sistemi e Informatica, CNR, Roma, Italy;Dipartimento di Matematica Pura ed Applicata, Università di L'Aquila, L'Aquila, Italy;Institut für Theoretische Informatik, ETH Zentrum, Zürich, Switzerland
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

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Abstract

In this paper we introduce the notion of best swap for a failing edge of a single source shortest paths tree (SPT) S(r) rooted in r in a weighted graph G = (V, E). Given an edge e ∈ S(r), an edge e′ ∈ E\{e} is a swap edge if the swap tree Se=e′ (r) obtained by swapping e with e′ in S(r) is a spanning tree of G. A best swap edge for a given edge e is a swap edge minimizing some distance functional between r and the set of nodes disconnected from the root after the edge e is removed. A swap algorithm with respect to some distance functional computes a best swap edge for every edge in S(r). We show that there exist fast swap algorithms (much faster than recomputing from scratch a new SPT) which also preserve the functionality of the affected SPT.