A Deterministic Distributed Algorithm for Weighted All Pairs Shortest Paths Through Pipelining.

We present a new pipelined approach to compute all pairs shortest paths (APSP) in a directed graph with nonnegative integer edge weights (including zero weights) in the CONGEST model in the distributed setting. Our deterministic distributed algorithm computes shortest paths of distance at most $\Delta$ for all pairs of vertices in at most $2 n \sqrt{\Delta} + 2n$ rounds, and more generally, it computes h-hop shortest paths for k sources in $2\sqrt{nkh} + n + k$ rounds. The algorithm is simple, and it has some novel features and a nontrivial analysis.It uses only the directed edges in the graph for communication. This algorithm can be used as a base within asymptotically faster algorithms that match or improve on the current best deterministic bound of $\tilde{O}(n^{3/2})$ rounds for this problem when edge weights are $O(n)$ or shortest path distances are $\tilde{O}(n^{3/2})$.

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