All Pairs Shortest Paths Hypothesis (APSP Hypothesis)
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Target Problem
Description
No randomized algorithm can solve APSP in $O(n^{3-\epsilon})$ time for $\epsilon > 0$ on $n$ node graphs with edge weights in $\{-n^c,\ldots,n^c\}$ and no negative cycles for large enough $c$.
Implies the following Hypothesis
Implied by the following Hypothesis
Computation Model
Word-RAM on $\log(n)$ bit words
Proven?
No
Year
References/Citation
http://people.csail.mit.edu/virgi/eccentri.pdf Hypothesis 3