Achieves (2k/3)-approximation for girth in weighted graphs in Õ(m + n^{1+2/k}) time for every k≥2, improving prior partial results, plus new fine-grained lower bounds for unweighted girth approximation.
New Routing Techniques and their Applications , booktitle =
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Tighter bounds for weighted and unweighted shortest cycle approximation
Achieves (2k/3)-approximation for girth in weighted graphs in Õ(m + n^{1+2/k}) time for every k≥2, improving prior partial results, plus new fine-grained lower bounds for unweighted girth approximation.