We consider the problem of computing all pairs shortest paths (APSP) and shortest paths for k sources in a weighted graph in the distributed Congest model. For graphs with non-negative integer edge weights (including zero weights) we build on a recent pipelined algorithm [1] to obtain aÕ(λ 1/4 · n 5/4 )-round bound for graphs with edge-weight at most λ, andÕ(n · △ 1/3 )-round bound for shortest path distances at most △. Additionally, we simplify some of the procedures in the earlier APSP algorithms for non-negative edge weights in [8, 2] . We also present results for computing h-hop shortest paths and shortest paths from k given sources. In other results, we present a randomized exact APSP algorithm for graphs with arbitrary edge weights that runs inÕ(n 4/3 ) rounds w.h.p. in n, which improves the previous bestÕ(n 3/2 ) bound, which is deterministic. We also present anÕ(n/ǫ 2 )-round deterministic (1 + ǫ) approximation algorithm for graphs with non-negative poly(n) integer weights (including zero edge-weights), improving results in [13, 11] that hold only for positive integer weights.
In a companion paper REF we build on the pipelined algorithm we present here to obtain an algorithm for non-negative integer edge-weights (including zero-weighted edges) that runs inÕ(n△ 1/3 ) rounds where the shortest path distances are at most △ and inÕ(n 5/4 λ 1/4 ) rounds when the edge weights are bounded by λ.
New and Simplified Distributed Algorithms for Weighted All Pairs Shortest Paths
ArXiv
ArXiv
Mathematics Computer Science