Minimum Witness Finding: Difference between revisions
(Created page with "{{DISPLAYTITLE:Minimum Witness Finding (Minimum Witness)}} == Description == Fix an instance of negative triangle with node sets $I, J, K$ and weight function $w$. Let $i \in I, j \in J, k \in K$. Recall that the triple $(i, j, k)$ is a negative triangle iff $(w(i, k) \odot w(k, j)) + w(i, j) < 0$. Fix a total ordering $<$ on the nodes in $K$ in the negative triangle instance. For any $i \in I, j \in J$, a node $k \in K$ is called a minimum witness for $(i, j)$ if $(i,...") |
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== Parameters == | == Parameters == | ||
$n$: number of vertices | |||
m: number of edges | |||
$m$: number of edges | |||
== Table of Algorithms == | == Table of Algorithms == | ||
Latest revision as of 08:27, 10 April 2023
Description
Fix an instance of negative triangle with node sets $I, J, K$ and weight function $w$. Let $i \in I, j \in J, k \in K$. Recall that the triple $(i, j, k)$ is a negative triangle iff $(w(i, k) \odot w(k, j)) + w(i, j) < 0$. Fix a total ordering $<$ on the nodes in $K$ in the negative triangle instance. For any $i \in I, j \in J$, a node $k \in K$ is called a minimum witness for $(i, j)$ if $(i, j, k)$ is a negative triangle but $(i, j, k')$ is not a negative triangle for all $k' < k$ according to the ordering.
Minimum Witness Finding is the problem of finding a negative triangle $(i,j,k)$ such that $k$ is a minimum witness for $(i,j)$.
Related Problems
Subproblem: All Pairs Minimum Witness
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: $T(n)$ where $n$ is the number of nodes in the graph then: from-time: $O(T(n))$ |
2018 | https://dl-acm-org.ezproxy.canberra.edu.au/doi/pdf/10.1145/3186893, Lemma 4.4 | link |