{"issue":"3","oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1504.07056","open_access":"1"}],"quality_controlled":"1","scopus_import":"1","title":"A deterministic almost-tight distributed algorithm for approximating single-source shortest paths","intvolume":"        50","language":[{"iso":"eng"}],"date_published":"2021-05-01T00:00:00Z","article_type":"original","year":"2021","publisher":"Society for Industrial & Applied Mathematics","day":"01","publication":"SIAM Journal on Computing","publication_status":"published","abstract":[{"text":"We present a deterministic (1+𝑜(1))-approximation (𝑛1/2+𝑜(1)+𝐷1+𝑜(1))-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the \\sf CONGEST model); here 𝑛 is the number of nodes in the network, 𝐷 is its (hop) diameter, and edge weights are positive integers from 1 to poly(𝑛). This is the first nontrivial deterministic algorithm for this problem. It also improves (i) the running time of the randomized (1+𝑜(1))-approximation 𝑂̃ (𝑛√𝐷1/4+𝐷)-time algorithm of Nanongkai [in Proceedings of STOC, 2014, pp. 565--573] by a factor of as large as 𝑛1/8, and (ii) the 𝑂(𝜖−1log𝜖−1)-approximation factor of Lenzen and Patt-Shamir's 𝑂̃ (𝑛1/2+𝜖+𝐷)-time algorithm [in Proceedings of STOC, 2013, pp. 381--390] within the same running time. (Throughout, we use 𝑂̃ (⋅) to hide polylogarithmic factors in 𝑛.) Our running time matches the known time lower bound of Ω(𝑛/log𝑛‾‾‾‾‾‾‾√+𝐷) [M. Elkin, SIAM J. Comput., 36 (2006), pp. 433--456], thus essentially settling the status of this problem which was raised at least a decade ago [M. Elkin, SIGACT News, 35 (2004), pp. 40--57]. It also implies a (2+𝑜(1))-approximation (𝑛1/2+𝑜(1)+𝐷1+𝑜(1))-time algorithm for approximating a network's weighted diameter which almost matches the lower bound by Holzer and Pinsker [in Proceedings of OPODIS, 2015, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, Germany, 2016, 6]. In 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 𝑛1+𝑜(1). We combine these techniques with many distributed algorithmic techniques, some of which are from problems that are not directly related to shortest paths, e.g., ruling sets [A. V. Goldberg, S. A. Plotkin, and G. E. Shannon, SIAM J. Discrete Math., 1 (1988), pp. 434--446], source detection [C. Lenzen and D. Peleg, in Proceedings of PODC, 2013, pp. 375--382], and partial distance estimation [C. Lenzen and B. Patt-Shamir, in Proceedings of PODC, 2015, pp. 153--162]. Our hop set construction also leads to single-source shortest paths algorithms in two other settings: (i) a (1+𝑜(1))-approximation 𝑛𝑜(1)-time algorithm on congested cliques, and (ii) a (1+𝑜(1))-approximation 𝑛𝑜(1)-pass 𝑛1+𝑜(1)-space streaming algorithm. The first result answers an open problem in [D. Nanongkai, in Proceedings of STOC, 2014, pp. 565--573]. The second result partially answers an open problem raised by McGregor in 2006 [List of Open Problems in Sublinear Algorithms: Problem 14].","lang":"eng"}],"_id":"11886","doi":"10.1137/16m1097808","author":[{"orcid":"0000-0002-5008-6530","full_name":"Henzinger, Monika H","first_name":"Monika H","id":"540c9bbd-f2de-11ec-812d-d04a5be85630","last_name":"Henzinger"},{"first_name":"Sebastian","full_name":"Krinninger, Sebastian","last_name":"Krinninger"},{"full_name":"Nanongkai, Danupon","first_name":"Danupon","last_name":"Nanongkai"}],"publication_identifier":{"issn":["0097-5397"],"eissn":["1095-7111"]},"date_updated":"2023-02-17T14:12:49Z","volume":50,"extern":"1","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"status":"public","page":"STOC16-98-STOC16-137","external_id":{"arxiv":["1504.07056"]},"citation":{"ama":"Henzinger MH, Krinninger S, Nanongkai D. A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. <i>SIAM Journal on Computing</i>. 2021;50(3):STOC16-98-STOC16-137. doi:<a href=\"https://doi.org/10.1137/16m1097808\">10.1137/16m1097808</a>","mla":"Henzinger, Monika H., et al. “A Deterministic Almost-Tight Distributed Algorithm for Approximating Single-Source Shortest Paths.” <i>SIAM Journal on Computing</i>, vol. 50, no. 3, Society for Industrial &#38; Applied Mathematics, 2021, pp. STOC16-98-STOC16-137, doi:<a href=\"https://doi.org/10.1137/16m1097808\">10.1137/16m1097808</a>.","short":"M.H. Henzinger, S. Krinninger, D. Nanongkai, SIAM Journal on Computing 50 (2021) STOC16-98-STOC16-137.","ieee":"M. H. Henzinger, S. Krinninger, and D. Nanongkai, “A deterministic almost-tight distributed algorithm for approximating single-source shortest paths,” <i>SIAM Journal on Computing</i>, vol. 50, no. 3. Society for Industrial &#38; Applied Mathematics, pp. STOC16-98-STOC16-137, 2021.","chicago":"Henzinger, Monika H, Sebastian Krinninger, and Danupon Nanongkai. “A Deterministic Almost-Tight Distributed Algorithm for Approximating Single-Source Shortest Paths.” <i>SIAM Journal on Computing</i>. Society for Industrial &#38; Applied Mathematics, 2021. <a href=\"https://doi.org/10.1137/16m1097808\">https://doi.org/10.1137/16m1097808</a>.","ista":"Henzinger MH, Krinninger S, Nanongkai D. 2021. A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. SIAM Journal on Computing. 50(3), STOC16-98-STOC16-137.","apa":"Henzinger, M. H., Krinninger, S., &#38; Nanongkai, D. (2021). A deterministic almost-tight distributed algorithm for approximating single-source shortest paths. <i>SIAM Journal on Computing</i>. Society for Industrial &#38; Applied Mathematics. <a href=\"https://doi.org/10.1137/16m1097808\">https://doi.org/10.1137/16m1097808</a>"},"month":"05","date_created":"2022-08-17T07:54:45Z","article_processing_charge":"No"}