{"abstract":[{"lang":"eng","text":"We present a deterministic (1+o(1))-approximation O(n1/2+o(1)+D1+o(1))-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the CONGEST model); here n is the number of nodes in the network and D is its (hop) diameter. This is the first non-trivial deterministic algorithm for this problem. It also improves (i) the running time of the randomized (1+o(1))-approximation Õ(n1/2D1/4+D)-time algorithm of Nanongkai [STOC 2014] by a factor of as large as n1/8, and (ii) the O(є−1logє−1)-approximation factor of Lenzen and Patt-Shamir’s Õ(n1/2+є+D)-time algorithm [STOC 2013] within the same running time. Our running time matches the known time lower bound of Ω(n1/2/logn + D) [Das Sarma et al. STOC 2011] modulo some lower-order terms, thus essentially settling the status of this problem which was raised at least a decade ago [Elkin SIGACT News 2004]. It also implies a (2+o(1))-approximation O(n1/2+o(1)+D1+o(1))-time algorithm for approximating a network’s weighted diameter which almost matches the lower bound by Holzer et al. [PODC 2012].\r\n\r\nIn achieving this result, we develop two techniques which might be of independent interest and useful in other settings: (i) a deterministic process that replaces the “hitting set argument” commonly used for shortest paths computation in various settings, and (ii) a simple, deterministic, construction of an (no(1), o(1))-hop set of size O(n1+o(1)). We combine these techniques with many distributed algorithmic techniques, some of which from problems that are not directly related to shortest paths, e.g. ruling sets [Goldberg et al. STOC 1987], source detection [Lenzen, Peleg PODC 2013], and partial distance estimation [Lenzen, Patt-Shamir PODC 2015]. Our hop set construction also leads to single-source shortest paths algorithms in two other settings: (i) a (1+o(1))-approximation O(no(1))-time algorithm on congested cliques, and (ii) a (1+o(1))-approximation O(no(1)logW)-pass O(n1+o(1)logW)-space streaming algorithm, when edge weights are in {1, 2, …, W}. The first result answers an open problem in [Nanongkai, STOC 2014]. The second result partially answers an open problem raised by McGregor in 2006 [<pre>sublinear.info</pre>, Problem 14]."}],"citation":{"ieee":"M. H. Henzinger, S. Krinninger, and D. Nanongkai, “A deterministic almost-tight distributed algorithm for approximating single-source shortest paths,” in <i>48th Annual ACM SIGACT Symposium on Theory of Computing</i>, Cambridge, MA, United States, 2016, pp. 489–498.","short":"M.H. Henzinger, S. Krinninger, D. Nanongkai, in:, 48th Annual ACM SIGACT Symposium on Theory of Computing, Association for Computing Machinery, 2016, pp. 489–498.","apa":"Henzinger, M. H., Krinninger, S., &#38; Nanongkai, D. (2016). A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. In <i>48th Annual ACM SIGACT Symposium on Theory of Computing</i> (pp. 489–498). Cambridge, MA, United States: Association for Computing Machinery. <a href=\"https://doi.org/10.1145/2897518.2897638\">https://doi.org/10.1145/2897518.2897638</a>","chicago":"Henzinger, Monika H, Sebastian Krinninger, and Danupon Nanongkai. “A Deterministic Almost-Tight Distributed Algorithm for Approximating Single-Source Shortest Paths.” In <i>48th Annual ACM SIGACT Symposium on Theory of Computing</i>, 489–98. Association for Computing Machinery, 2016. <a href=\"https://doi.org/10.1145/2897518.2897638\">https://doi.org/10.1145/2897518.2897638</a>.","ama":"Henzinger MH, Krinninger S, Nanongkai D. A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. In: <i>48th Annual ACM SIGACT Symposium on Theory of Computing</i>. Association for Computing Machinery; 2016:489-498. doi:<a href=\"https://doi.org/10.1145/2897518.2897638\">10.1145/2897518.2897638</a>","ista":"Henzinger MH, Krinninger S, Nanongkai D. 2016. A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. 48th Annual ACM SIGACT Symposium on Theory of Computing. STOC: Symposium on Theory of Computing, 489–498.","mla":"Henzinger, Monika H., et al. “A Deterministic Almost-Tight Distributed Algorithm for Approximating Single-Source Shortest Paths.” <i>48th Annual ACM SIGACT Symposium on Theory of Computing</i>, Association for Computing Machinery, 2016, pp. 489–98, doi:<a href=\"https://doi.org/10.1145/2897518.2897638\">10.1145/2897518.2897638</a>."},"main_file_link":[{"url":"https://arxiv.org/abs/1504.07056","open_access":"1"}],"oa_version":"Preprint","title":"A deterministic almost-tight distributed algorithm for approximating single-source shortest paths","author":[{"full_name":"Henzinger, Monika H","first_name":"Monika H","orcid":"0000-0002-5008-6530","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger"},{"full_name":"Krinninger, Sebastian","last_name":"Krinninger","first_name":"Sebastian"},{"full_name":"Nanongkai, Danupon","first_name":"Danupon","last_name":"Nanongkai"}],"quality_controlled":"1","date_published":"2016-06-01T00:00:00Z","year":"2016","month":"06","language":[{"iso":"eng"}],"extern":"1","publication_identifier":{"isbn":["978-145034132-5"],"issn":["0737-8017"]},"doi":"10.1145/2897518.2897638","_id":"11866","scopus_import":"1","page":"489 - 498","type":"conference","article_processing_charge":"No","day":"01","oa":1,"date_updated":"2023-02-17T10:32:23Z","date_created":"2022-08-16T09:19:31Z","external_id":{"arxiv":["1504.07056"]},"conference":{"location":"Cambridge, MA, United States","end_date":"2016-06-21","start_date":"2016-06-19","name":"STOC: Symposium on Theory of Computing"},"publisher":"Association for Computing Machinery","publication":"48th Annual ACM SIGACT Symposium on Theory of Computing","publication_status":"published","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}