TY - GEN

T1 - Incremental maintenance of the 5-edge-connectivity classes of a graph

AU - Dinitz, Yefim

AU - Nossenson, Ronit

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2000.

PY - 2000/1/1

Y1 - 2000/1/1

N2 - 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).

AB - 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).

UR - http://www.scopus.com/inward/record.url?scp=84927804736&partnerID=8YFLogxK

U2 - 10.1007/3-540-44985-X

DO - 10.1007/3-540-44985-X

M3 - Conference contribution

AN - SCOPUS:84927804736

SN - 3540676902

SN - 9783540676904

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 272

EP - 285

BT - Algorithm Theory - SWAT 2000 - 7th Scandinavian Workshop on Algorithm Theory, 2000, Proceedings

A2 - Halldórsson, Magnús M.

PB - Springer Verlag

T2 - 7th Scandinavian Workshop on Algorithm Theory, SWAT 2000

Y2 - 5 July 2000 through 7 July 2000

ER -