A deterministic almost-tight distributed algorithm for approximating single-source shortest paths
Monika Rauch Henzinger, Sebastian Forster, Danupon Nanongkai · 2016
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].