Distributed Weighted All Pairs Shortest Paths Through Pipelining
2019 IEEE International Parallel and Distributed Processing Symposium (IPDPS)(2019)
摘要
We present new results for the distributed computation of all pairs shortest paths (APSP) in the CONGEST model in an n-node graph with moderate non-negative integer weights. Our methods can handle zero-weight edges which are known to present difficulties for distributed APSP algorithms. The current best deterministic distributed algorithm in the CONGEST model that handles zero weight edges is the Õ(n
3/2
)-round algorithm of Agarwal et al. [3] that works for arbitrary edge weights. Our new deterministic algorithms run in O(W
1/4
· n
5/4
) rounds in graphs with non-negative integer edge-weight at most W, and in Õ(n·Δ
1/3
) rounds for shortest path distances at most Δ. These algorithms are built on top of a new pipelined algorithm we present for this problem that runs in at most 2n√Δ + 2n rounds. Additionally, we show that the techniques in our results simplify some of the procedures in the earlier APSP algorithms for non-negative edge weights in [3], [13]. We also present new results for computing h-hop shortest paths from k given sources, including the notion of consistent h-hop shortest path trees, and we present an O(n/ϵ
2
)-round deterministic (1+ϵ) approximation algorithm for graphs with non-negative poly(n) integer weights, improving results in [16], [18] that hold only for positive integer weights.
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关键词
Weighted Shortest Paths,Distributed Algorithms,Deterministic Algorithms,Blocker Set
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