An incremental distributed algorithm for computing biconnected components
This paper describes a distributed algorithm for computing biconnected components of a dynamically changing graph. Our algorithm has worst case communication complexity of O(b + c) messages for edge insertion and O(b′ + c) messages for edge removal, and worst case time complexity of O(c) for both operations, where c is the maximum number of biconnected components in any of the connected components during the operation, b is the number of nodes in the biconnected component containing the new edge, and b′ is the number of nodes in the biconnected component in which the update is being processed.
The algorithm is presented in two stages. First, a serial algorithm is presented in which topology updates occur one at a time. Then, building on the serial algorithm, an algorithm is presented in which concurrent update requests are serialized within each connected component. The problem is motivated by the need to implement causal ordering of messages efficiently in a dynamically changing communication structure.
Keywordsbiconnected components distributed graph algorithms dynamic configuration
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