Reduction from Min-Weight k-Clique to Minimum Weight k-Cycle

FROM: Min-Weight k-Clique TO: Minimum Weight k-Cycle

Implications

if: to-time: $O(nm^{\lceil k/{2} \rceil / \lambda - \epsilon})$ for any $\epsilon > {0}$ for $m = \Theta(n^{1+{1}/(\lambda - {1})}) edges and $n$ nodes where $\lambda = k - \lceil k/{2} \rceil + {1}$
then: from-time: $O(n^{k - \epsilon})$ for some $\epsilon > {0}$

Year

2018

Reference

Andrea Lincoln, Virginia Vassilevska Williams, and R. Ryan Williams. Tight hardness for shortest cycles and paths in sparse graphs. In Proc. SODA, page to appear, 2018.

https://arxiv.org/pdf/1712.08147v2.pdf, Corollary 4.2