Abstract
This paper presents efficient distributed algorithms on an asynchronous network for the following problems: finding bi-connected components, finding cutpoints, finding bridges, testing for bi-connectedness and finding strongly connected components of a directed graph defined on a network. All these distributed algorithms use a depth-first search tree having an arbitrary processor in the network as its root. The communication complexity of these algorithms is O(nlogn+e) and their ideal-time complexity is O(nG(n)), where n and e represent the numbers of processors and links, respectively, and G(n) is almost a constant. It is shown also that a lower bound for the communication complexity of the five problems is O(e) and a lower bound for their ideal-time complexity is O(n).
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