A Deterministic Almost-Tight Distributed Algorithm for Approximating Single-Source Shortest Paths

Understand

We present a deterministic $(1+o(1))$-approximation $(n^{1/2+o(1)}+D^{1+o(1)})$-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 $\tilde O(n^{1/2}D^{1/4}+D)$-time algorithm of Nanongkai [STOC 2014] by a factor of as large as $n^{1/8}$, and (ii) the $O(\epsilon^{-1}\log \epsilon^{-1})$-approximation factor of Lenzen and Patt-Shamir's $\tilde O(n^{1/2+\epsilon}+D)$-time algorithm [STOC 2013] within the same running time.
• Our running time matches the known time lower bound of $\Omega(n^{1/2}/\log n + D)$ [Elkin STOC 2004] up to subpolynomial factors, thus essentially settling the status of this problem which was raised at least a decade ago [Elkin SIGACT News 2004].