All-Nodes Median Parity (Vertex Centrality)
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Description
Given a graph $G = (V, E)$, compute $Med(v) (\mod 2)$ for all $v\in V$, where $Med(v) := \sum\limits_{w\in V} d(v, w)$
Related Problems
Related: Eccentricity, Betweenness Centrality, Approximate Betweenness Centrality, Positive Betweenness Centrality, Directed All-Nodes Positive Betweenness Centrality, Undirected All-Nodes Positive Betweenness Centrality, Reach Centrality, Directed All-Nodes Reach Centrality, Undirected All-Nodes Reach Centrality, Approximate Reach Centrality
Parameters
$n$: number of nodes
$m$: number of edges
Table of Algorithms
Currently no algorithms in our database for the given problem.
Reductions FROM Problem
| Problem | Implication | Year | Citation | Reduction |
|---|---|---|---|---|
| Negative Triangle Detection | if: to-time: $\tilde{O}(T(n,M))$ for $n$-node $m$-edge graph with integer weights in $(-M, M)$ then: from-time: $\tilde{O}T(n,M))$ |
2015 | https://epubs.siam.org/doi/10.1137/1.9781611973730.112, Lemma 2.5 | link |
| Directed, Weighted APSP | if: to-time: Truly subcubic then: from-time: Truly subcubic |
2015 | https://epubs.siam.org/doi/10.1137/1.9781611973730.112, Corollary 2.1 | link |
| Undirected, Weighted APSP | if: to-time: Truly subcubic then: from-time: Truly subcubic |
2015 | https://epubs.siam.org/doi/10.1137/1.9781611973730.112, Corollary 2.1 | link |