Negative Triangle Listing (Graph Triangle Problems)
Revision as of 10:28, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Negative Triangle Listing (Graph Triangle Problems)}} == Description == Given an $n$ node graph $G = (V, E)$ with edge weights $w: E \rightarrow W$, list the negative triangles, i.e. three vertices that form a triangle with total edge weights summing to a negative number. == Related Problems == Generalizations: Negative Triangle Search Related: Negative Triangle Detection, Nondecreasing Triangle, Minimum Triangle, Triangle in Unweig...")
Description
Given an $n$ node graph $G = (V, E)$ with edge weights $w: E \rightarrow W$, list the negative triangles, i.e. three vertices that form a triangle with total edge weights summing to a negative number.
Related Problems
Generalizations: Negative Triangle Search
Related: Negative Triangle Detection, Nondecreasing Triangle, Minimum Triangle, Triangle in Unweighted Graph, Triangle Detection, Triangle Collection*
Parameters
n: number of vertices m: number of edges
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions TO Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Negative Triangle Detection | if: to-time: $O(n^{3-\epsilon}\log^c M)$ for some $\epsilon > {0}$ and where $M$ is the maxint of $R$ then: from-time: $O(n^{3-\epsilon'}\log^c M)$ for some $\epsilon' > {0}$ for listing $\Delta = O(n^{3-\delta})$ negative triangles with fixed $\delta > {0}$ |
2018 | https://dl-acm-org.ezproxy.canberra.edu.au/doi/pdf/10.1145/3186893, Theorem 4.3 | link |