Corpus ID: 12361070

An expected-case sub-cubic solution to the all-pairs shortest path problem in R

@article{McAuley2009AnES,
  title={An expected-case sub-cubic solution to the all-pairs shortest path problem in R},
  author={Julian McAuley and T. Caetano},
  journal={ArXiv},
  year={2009},
  volume={abs/0912.0975}
}
  • Julian McAuley, T. Caetano
  • Published 2009
  • Mathematics, Computer Science
  • ArXiv
  • It has been shown by Alon et al. that the so-called 'all-pairs shortest-path' problem can be solved in O((MV)^2.688 * log^3(V)) for graphs with V vertices, with integer distances bounded by M. We solve the more general problem for graphs in R (assuming no negative cycles), with expected-case running time O(V^2.5 * log(V)). While our result appears to violate the Omega(V^3) requirement of "Funny Matrix Multiplication" (due to Kerr), we find that it has a sub-cubic expected time solution subject… CONTINUE READING
    Faster Funny Matrix Multiplication for the All-Pairs Shortest Paths Problem

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