Monochromatic Triangles, Triangle Listing and APSP

  title={Monochromatic Triangles, Triangle Listing and APSP},
  author={V. Williams and Yinzhan Xu},
  journal={2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)},
  • V. Williams, Yinzhan Xu
  • Published 2020
  • Computer Science, Mathematics
  • 2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)
  • All-Pairs Shortest Paths (APSP) is one of the most basic problems in graph algorithms. Given an $n$-node directed or undirected graph with integer weights in $\{-n^{c}, \ldots, n^{c}\}$ and no negative cycles, APSP asks to compute the shortest paths distance between every pair of vertices. The fastest known algorithm for APSP runs in $n^{3}/2^{\Theta(\sqrt{\log n})}$ time [Williams'14], and no truly subcubic time algorithms are known. One of the main hypotheses in fine-grained complexity is… CONTINUE READING


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