Diameter 3 vs 7: Difference between revisions

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(Created page with "{{DISPLAYTITLE:Diameter 3 vs 7 (Graph Metrics)}} == Description == Given a graph $G = (V, E)$, distinguish between diameter 3 and diameter 7. In other words, approximate diameter within a factor of $9/4-\epsilon$. == Related Problems == Generalizations: Approximate Diameter Related: Median, Radius, Diameter, Diameter 2 vs 3, Decremental Diameter, 1-sensitive (4/3)-approximate decremental diameter, 1-sensitive decremental diameter, ...")
 
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== Parameters ==  
== Parameters ==  


<pre>n: number of nodes
$n$: number of nodes
m: number of edges</pre>
 
$m$: number of edges


== Table of Algorithms ==  
== Table of Algorithms ==  

Latest revision as of 07:53, 10 April 2023

Description

Given a graph $G = (V, E)$, distinguish between diameter 3 and diameter 7. In other words, approximate diameter within a factor of $9/4-\epsilon$.

Related Problems

Generalizations: Approximate Diameter

Related: Median, Radius, Diameter, Diameter 2 vs 3, 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
3-OV If: to-time: $O(N^{({3}/{2}-\epsilon)}$ where $N=n^{2} d^{2}$ and $\epsilon > {0}$
Then: from-time: $n^{3-{2}\epsilon} poly(d)$
2018 https://dl.acm.org/doi/pdf/10.1145/3188745.3188950 link