Approximate Reach Centrality (Vertex Centrality)

Description

The reach centrality of a node $w$ is the smallest distance $r$ such that any $s-t$ shortest path passing through $w$ has either $s$ or $t$ in the ball of radius $r$ around $w$.

Approximate reach centrality is the approximation version of the problem.

Related Problems

Generalizations: Reach Centrality

Related: Eccentricity, All-Nodes Median Parity, Betweenness Centrality, Approximate Betweenness Centrality, Positive Betweenness Centrality, Directed All-Nodes Positive Betweenness Centrality, Undirected All-Nodes Positive Betweenness Centrality, Directed All-Nodes Reach Centrality, Undirected All-Nodes 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
CNF-SAT	if: to-time: $O(m^{2-\epsilon})$ for some $\epsilon > {0}$ then: from-time: $O*({2}^{({1}-\delta)n})$ for some $\delta > {0}$	2015	https://epubs.siam.org/doi/10.1137/1.9781611973730.112, Corollary 4.2	link
CNF-SAT	if: to-time: $O(m^{2-\epsilon})$ then: from-time: $O*({2}^{({1}-\epsilon/{2})n})$	2015	https://epubs.siam.org/doi/10.1137/1.9781611973730.112, Theorem 4.4	link