A Distributed Algorithm for Minimum-Weight Spanning Trees

Abstract

A distributed algorithm is presented that constructs the minimum-weight spanning tree in a connected undirected graph with distinct edge weights. A processor exists at each node of the graph, knowing initially only the weights of the adjacent edges. The processors obey the same algorithm and exchange messages with neighbors until the tree is constructed. The total number of messages required for a graph of N nodes and E edges is at most 5N log2N + 2E, and a message contains at most one edge weight plus log28N bits. The algorithm can be initiated spontaneously at any node or at any subset of nodes.

Merging Clustering Algorithms in Mobile Ad Hoc Networks

“…We showed the implementation of the algorithm and analyzed its time and message complexity. Our algorithm has a similar but more simplified structure than Gallagher's Algorithm [5]. The algorithm has a lower complexity and also we aim at forming clusters whereas the latter tries to find an MST.…”

“…The resulting clusters can overlap and nodes in the same cluster may not be directly connected [2]. Gallagher, Humblet, Spira's Distributed Algorithm [5] and Srivastava, Ghosh's k-tree core Algorithm [6] are two algorithms which construct distributed minimum spanning trees in MANETs.…”

“…Gallagher, Humblet and Spira's Distributed Algorithm: Gallagher, Humblet and Spira [5] proposed a distributed algorithm which determines a minimumweight spanning tree for an undirected graph that has distinct finite weights for every edge. Aim of the algorithm is to combine small fragments into larger fragments with outgoing edges.…”

“…A message contains at most one edge weight and log 2 8N bits. A worst case time for this algorithm is O(NlogN) [5].…”

Distributed Computation of Maximum Lifetime Spanning Subgraphs in Sensor Networks

“…They also emphasise the importance of considering the minmax energy metric rather than the more often addressed minimum total energy metric for maximising network lifetime. For a distributed implementation, Kang and Poovendran rely on distributed methods for constructing minimum spanning trees (MST), such as the algorithm of Gallager, Humblet and Spira [5]. These techniques are, however, rather involved, and we complement this work by suggesting a much simpler distributed method for constructing general spanning subgraphs with minmax edge costs.…”