Incremental maintenance of the 5-edge-connectivity classes of a graph

Yefim Dinitz, Ronit Nossenson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

Two vertices of an undirected graph are called k-edge-conn-ected if there exist k edge-disjoint paths between them. The equivalence classes of this relation are called k-edge-connected classes, or k-classes for short. This paper shows how to check whether two vertices belong to the same 5-class of an arbitrary connected graph that is undergoing edge insertions. For this purpose we suggest (i) a full description of the 4-cuts of an arbitrary graph and (ii) a representation of the k-classes, 1 ≤ k ≤ 5, of size linear in n-the number of vertices of the graph; these representations can be constructed in a polynomial time. Using them, we suggest an algorithm for incremental maintenance of the 5-classes. The total time for a sequence of m Edge-Insert updates and q Same-5-Class? queries is O(q + m + n · log2n); the worst-case time per query is O(1).

Original languageEnglish
Title of host publicationAlgorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings
EditorsMagnús M. Halldórsson
PublisherSpringer Verlag
Pages272-285
Number of pages14
ISBN (Print)3540676902, 9783540676904
DOIs
StatePublished - 1 Jan 2000
Event7th Scandinavian Workshop on Algorithm Theory, SWAT 2000 - Bergen, Norway
Duration: 5 Jul 20007 Jul 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1851
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th Scandinavian Workshop on Algorithm Theory, SWAT 2000
Country/TerritoryNorway
CityBergen
Period5/07/007/07/00

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