Bridge-connectivity Augmenting Problem with a Partition Constraint

Abstract

This paper considers the augmentation problem of an undirected graph with k partitions of its vertices. The main issue is how to add a set of edges with the smallest possible cardinality so that the resulting graph is 2-edge-connected, i.e., bridge-connected, while maintaining the partition constraint. To solve this problem, we propose a simple linear-time algo- rithm. We show that the algorithm runs in O(log n) parallel time on an EREW PRAM using a linear number of processors.