A Simple Deterministic Distributed Mst Algorithm With Near-Optimal Time And Message Complexities Foreword
PODC(2020)
摘要
Distributed minimum spanning tree (MST) problem is one of the most central and fundamental problems in distributed graph algorithms. Kutten and Peleg [KP98] devised an algorithm with running time O(D + root n . log*n), where D is the hop-diameter of the input n-vertexm-edge graph, and with message complexity O(m + n(3/2)). Peleg and Rubinovich [PR99] showed that the running time of the algorithm of [KP98] is essentially tight, and asked if one can achieve near-optimal running time together with near-optimal message complexity.In a recent breakthrough, Pandurangan et al. [PRS16] answered this question in the affirmative, and devised a randomized algorithm with time (O) over tilde (D + root n) and message complexity (O) over tilde (m). They asked if such a simultaneous time- and message-optimality can be achieved by a deterministic algorithm.In this paper, building upon the work of [PRS16], we answer this question in the affirmative, and devise a deterministic algorithm that computes MST in time O((D + root n) . logn), using O(m . logn + n logn . log*n) messages. The polylogarithmic factors in the time and message complexities of our algorithm are significantly smaller than the respective factors in the result of [PRS16]. Also, our algorithm and its analysis are very simple and self-contained, as opposed to rather complicated previous sublinear-time algorithms [GKP98, KP98, Elk04b, PRS16].
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关键词
Distributed graph algorithms, minimum spanning tree
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