Derandomizing Distributed Algorithms with Small Messages: Spanners and Dominating Set

This paper presents improved deterministic distributed algorithms, with O(logn)-bit messages, for some basic graph problems. The common ingredient in our results is a deterministic distributed algorithm for computing a certain hitting set, which can replace the random part of a number of standard randomized distributed algorithms. This deterministic hitting set algorithm itself is derived using a simple method of conditional expectations. As one main end-result of this derandomized hitting set, we get a deterministic distributed algorithm with round complexity 2O( √ log n·log log n) for computing a (2k − 1)-spanner of size Õ(n1+1/k). This improves considerably on a recent algorithm of Grossman and Parter [DISC’17] which needs O(n1/2−1/k · 2) rounds. We also get a 2O( √ log n·log log n)-round deterministic distributed algorithm for computing an O(log2 n)-approximation of minimum dominating set; all prior algorithms for this problem were either randomized or required large messages. 2012 ACM Subject Classification Theory of computation → Distributed algorithms

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