Reduction from Triangle Detection to Dynamic Bipartite Maximum-Weight Matching
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FROM: Triangle Detection TO: Dynamic Bipartite Maximum-Weight Matching
Description
Implications
let $\gamma = (w-{1})/(w+{1}) \in ({1}/{3},{0.408})$
if: to-time: $O(m^{2\gamma-\epsilon})$ update and query times even after O(m^{1+\gamma-\epsilon}) preprocessing time for any $\epsilon > {0}$
then: Strong Triangle is false
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.