A DETERMINISTIC ALMOST-TIGHT DISTRIBUTED ALGORITHM FOR APPROXIMATING SINGLE-SOURCE SHORTEST PATHS.

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος:	A DETERMINISTIC ALMOST-TIGHT DISTRIBUTED ALGORITHM FOR APPROXIMATING SINGLE-SOURCE SHORTEST PATHS.
Συγγραφείς:	HENZINGER, MONIKA, KRINNINGER, SEBASTIAN, NANONGKAI, DANUPON
Πηγή:	SIAM Journal on Computing; 2021, Vol. 50 Issue 3, p98-137, 40p
Θεματικοί όροι:	Algorithms, Deterministic algorithms, Distributed algorithms, Deterministic processes, Mathematics
Γεωγραφικοί όροι:	Thailand, Germany
Περίληψη:	We present a deterministic (1+o(1))-approximation O(n^1/2+o(1) + D^1+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(√n1/2D^1/4+D)-time algorithm of Nanongkai [STOC 2014] by a factor of as large as n^1/8, and (ii) the O(є^-1logє^-1)-approximation factor of Lenzen and Patt-Shamir's Õ(n^1/2+є+D)-time algorithm [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/log n + 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 O(n^1/2+o(1)+D^1+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 (n^o(1), o(1))-hop set of size n^1+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 n^o(1)-pass n^1+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]. [ABSTRACT FROM AUTHOR]
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Βάση Δεδομένων:	Complementary Index

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