This paper presents improved deterministic distributed algorithms, with O(log n)-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 2^O(sqrt{log n * log log n}) for computing a (2k-1)-spanner of size O~(n^{1+1/k}). This improves considerably on a recent algorithm of Grossman and Parter [DISC'17] which needs O(n^{1/2-1/k} * 2^k) rounds. We also get a 2^O(sqrt{log n * log log n})-round deterministic distributed algorithm for computing an O(log^2 n)-approximation of minimum dominating set; all prior algorithms for this problem were either randomized or required large messages.
@InProceedings{ghaffari_et_al:LIPIcs.DISC.2018.29, author = {Ghaffari, Mohsen and Kuhn, Fabian}, title = {{Derandomizing Distributed Algorithms with Small Messages: Spanners and Dominating Set}}, booktitle = {32nd International Symposium on Distributed Computing (DISC 2018)}, pages = {29:1--29:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-092-7}, ISSN = {1868-8969}, year = {2018}, volume = {121}, editor = {Schmid, Ulrich and Widder, Josef}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2018.29}, URN = {urn:nbn:de:0030-drops-98181}, doi = {10.4230/LIPIcs.DISC.2018.29}, annote = {Keywords: Distributed Algorithms, Derandomization, Spanners, Dominating Set} }
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