A Faster Distributed Single-Source Shortest Paths Algorithm
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We devise new algorithms for the single-source shortest paths problem in the CONGEST model of distributed computing. While close-to-optimal solutions, in terms of the number of rounds spent by the algorithm, have recently been developed for computing single-source shortest paths approximately, the fastest known exact algorithms are still far away from matching the lower bound of Ω̃ (√(n) + D) rounds by Peleg and Rubinovich [SICOMP'00], where n is the number of nodes in the network and D is its diameter. The state of the art is Elkin's randomized algorithm [STOC'17] that performs Õ(n^2/3 D^1/3 + n^5/6) rounds. We significantly improve upon this upper bound with our two new randomized algorithms, the first performing Õ (√(n D)) rounds and the second performing Õ (√(n) D^1/4 + n^3/5 + D) rounds.
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