Minimizing communication in all-pairs shortest paths

Edgar Solomonik, Aydin Buluç, James Demmel

Research output: Contribution to conferencePaperpeer-review


We consider distributed memory algorithms for the all-pairs shortest paths (APSP) problem. Scaling the APSP problem to high concurrencies requires both minimizing inter-processor communication as well as maximizing temporal data locality. The 2.5D APSP algorithm, which is based on the divide-and-conquer paradigm, satisfies both of these requirements: it can utilize any extra available memory to perform asymptotically less communication, and it is rich in semiring matrix multiplications, which have high temporal locality. We start by introducing a block-cyclic 2D (minimal memory) APSP algorithm. With a careful choice of block-size, this algorithm achieves known communication lower-bounds for latency and bandwidth. We extend this 2D block-cyclic algorithm to a 2.5D algorithm, which can use c extra copies of data to reduce the bandwidth cost by a factor of c1/2, compared to its 2D counterpart. However, the 2.5D algorithm increases the latency cost by c1/2. We provide a tighter lower bound on latency, which dictates that the latency overhead is necessary to reduce bandwidth along the critical path of execution. Our implementation achieves impressive performance and scaling to 24,576 cores of a Cray XE6 supercomputer by utilizing well-tuned intra-node kernels within the distributed memory algorithm.

Original languageEnglish (US)
Number of pages12
StatePublished - 2013
Externally publishedYes
Event27th IEEE International Parallel and Distributed Processing Symposium, IPDPS 2013 - Boston, MA, United States
Duration: May 20 2013May 24 2013


Other27th IEEE International Parallel and Distributed Processing Symposium, IPDPS 2013
Country/TerritoryUnited States
CityBoston, MA


  • 2.5D algorithms
  • all-pairs shortest paths
  • communication-avoiding algorithms

ASJC Scopus subject areas

  • Software


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