On the communication complexity of strong time-optimal distributed algorithms

Authors:
Stefan Dobrev;Peter Ružička
Affiliations:
Institute of Informatics, Faculty of Mathematics and Physics, Comenius University, Mlynská dolina, 842 15 Bratislava, Slovak Republic;Institute of Informatics, Faculty of Mathematics and Physics, Comenius University, Mlynská dolina, 842 15 Bratislava, Slovak Republic
Venue:
Nordic Journal of Computing
Year:
1998

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Abstract

In this paper we introduce the notion of time optimality in the strong sense and we investigate the communication complexity of strong time-optimal distributed algorithms. We show that a strong time-optimal algorithm solving the MST problem on networks with n nodes and m links interchanges at least (m-n)2 messages. We also present an Θ(m2) bound on communication complexity for strong time-optimal algorithms solving the gossip problem. As a consequence, similar results can be shown for other interesting problems on arbitrary networks, such as electing a leader, determining the median and the center, computing the diameter and others.