All Pairs Shortest Paths Hypothesis (APSP Hypothesis)
Revision as of 11:30, 15 February 2023 by Admin (talk | contribs) (Created page with "== Target Problem == APSP == 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.csa...")
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