Published 2020
“…Starting from the hypothesis that the minimum weight (2ℓ+ 1)-Clique problem in edge weighted graphs requires n2ℓ+1-o(1) time, we prove that for all
sparsities of the form m = Q(n1+1/ℓ), there is no O(n2 +mn1-ϵ ) time algorithm for e > 0 for any of the below problems Minimum Weight (2ℓ + 1)-Cycle in a directed weighted graph, Shortest Cycle in a directed weighted graph, APSP in a directed or undirected weighted graph, Radius (or Eccentricities) in a directed or undirected weighted graph, Wiener index of a directed or undirected weighted graph, Replacement Paths in a directed weighted graph, Second Shortest Path in a directed weighted graph, Betweenness Centrality of a given node in a directed weighted graph. …”
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