A simple deterministic distributed MST algorithm, with near-optimal time and message complexities

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 + √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 Õ (D + √n) and message complexity Õ (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 + √n) · log n), using O(m · log n + n log n · 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].