Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems

B. Awerbuch
1987 Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87  
This paper develops linear time d'etributed algorithms for a class of problems in an asynchronous communication network. Those problems include Minimum-Weight Spanning Tree (MST), Leader Election, counting the number of network nodes, and computing a senaitive decomposable function (e.g. majority, parity, maximum, OR, AND). The main problem considered is ,the problem of finding the MST. This problem, which has been known for at least 9 years, is one of the most fundamental and the most studied
more » ... roblems in the field of distributed network algorithms. Any algorithm for any one of the problems ,above requires at least n(E-tVlogV) communication and and n(V) time in the genera1 network. In this paper, we present new algorithms, which achieve those lower bounds. The best previous algorithm requires 8(E+ Vlog V) in communication and e( V.log' V) in time. Our result enables to improve algo:rithms for many other problems in distributed computing, achieving lower bounds on their communication and time complexities, t Supported by Chaim Weizmann Postdoctoral Fellowship and Air Force contract TNDGAFOSR-860078. Permission to copy without fee all or part of tlhis material is granted provided that the copies are not made or 'distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specfic permission. 0 1987 ACM 0-89791-221-7/87/000&0230 75t
doi:10.1145/28395.28421 dblp:conf/stoc/Awerbuch87 fatcat:3zb7nf4pf5ebnjeoovifxoeume