Algorithms, Reductions and Equivalences for Small Weight Variants of All-Pairs Shortest Paths

11 Feb 2021 Timothy M. Chan Virginia Vassilevska Williams Yinzhan Xu

APSP with small integer weights in undirected graphs [Seidel'95, Galil and Margalit'97] has an $\tilde{O}(n^\omega)$ time algorithm, where $\omega<2.373$ is the matrix multiplication exponent. APSP in directed graphs with small weights however, has a much slower running time that would be $\Omega(n^{2.5})$ even if $\omega=2$ [Zwick'02]... (read more)

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  • DATA STRUCTURES AND ALGORITHMS
  • COMPUTATIONAL COMPLEXITY