Reduction from Triangle Detection to Dynamic st-Reach
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FROM: Triangle Detection TO: Dynamic st-Reach
Description
Implications
assume: SETH
then: for any fixed constants $\epsilon > {0}$, $c_1,c_2 \in ({0},{1})$, on graphs with $n$ nodes $|S|=\tilde{\Theta}(n^{c_1})$, $|T|=\tilde{\Theta(n^{c_2})}$, $m=O(n)$ edges, and capacaties in $\{1,\cdots,n\}$, target cannot be solved in $O((|S|T|m)^{1-\epsilon})$
Year
2014
Reference
Abboud, Amir, and Virginia Vassilevska Williams. "Popular conjectures imply strong lower bounds for dynamic problems." In 2014 IEEE 55th Annual Symposium on Foundations of Computer Science, pp. 434-443. IEEE, 2014.