# Diameter 2 vs 3 (Graph Metrics)

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## Description

Given a graph $G = (V, E)$, distinguish between diameter 2 and diameter 3. In other words, approximate diameter within a factor of $4/3-\epsilon$.

## Related Problems

Generalizations: Approximate Diameter

Related: Median, Radius, Diameter, Diameter 3 vs 7, Decremental Diameter, 1-sensitive (4/3)-approximate decremental diameter, 1-sensitive decremental diameter, constant sensitivity (4/3)-approximate incremental diameter, 1-sensitive (4/3)-approximate decremental eccentricity

## 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 |
---|---|---|---|---|

OV | If: to-time: $O(N^{({2}-\epsilon)})$ where $N = nd$ and $V,E = O(n)$ Then: from-time: $O((nd)^{({2}-\epsilon)}) \leq n^{({2}-\epsilon)} poly(d)$ where {2} sets of $n$ $d$-dimensional vectors |
2013 | https://people.csail.mit.edu/virgi/diam.pdf | link |