Dynamic bottleneck optimization for k-edge and 2-vertex connectivity

Authors:
Orestis A. Telelis;Vassilis Zissimopoulos
Affiliations:
Department of Computer Science, University of Aarhus, Denmark;Department of Informatics and Telecommunications, University of Athens, Greece
Venue:
Information Processing Letters
Year:
2008

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Abstract

We consider the problem of updating efficiently the minimum value b over a weighted graph, so that edges with a cost less than b induce a spanning subgraph satisfying a k-edge or 2-vertex connectivity constraint, when the cost of an edge of the graph is updated. Our results include update algorithms of almost linear time (up to poly-logarithmic factors) in the number of vertices for all considered connectivity constraints (for fixed k), and a worst case construction showing that these algorithms are almost optimal in their class.