# 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