Abstract
Given an $n$-vertex $m$-edge graph $G$ with nonnegative edge-weights, a shortest cycle is one minimizing the sum of the weights on its edges. The girth of $G$ is the weight of a shortest cycle. We ...
Highlights
The exciting program of “Hardness in P” aims at proving the exact time-complexity of fundamental, polynomial-time solvable problems in computer science
We recall that the girth of a given graph G is the minimum weight of a cycle in G – with the weight of a cycle being defined as the sum of the weights on its edges
For dense graphs this parameter can be computed in time O(n3), and Vassilevska Williams and Williams [19] proved a bunch of combinatorial subcubic equivalences between Girth and other path and matrix problems
Summary
The exciting program of “Hardness in P” aims at proving (under plausible complexity theoretic conjectures) the exact time-complexity of fundamental, polynomial-time solvable problems in computer science. We recall that the girth of a given graph G is the minimum weight of a cycle in G – with the weight of a cycle being defined as the sum of the weights on its edges (see Sec. 2 for any undefined terminology in this introduction). For dense graphs this parameter can be computed in time O(n3), and Vassilevska Williams and Williams [19] proved a bunch of combinatorial subcubic equivalences between Girth and other path and matrix problems. We answer to this above question in the affirmative
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