constant sensitivity (4/3)-approximate incremental diameter (Graph Metrics)
Revision as of 10:28, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:constant sensitivity (4/3)-approximate incremental diameter (Graph Metrics)}} == Description == Approximate the diameter of a graph decrementally within a factor of 4/3, with a constant sensitivity of $K(\epsilon, t)$, i.e. when a $K(\epsilon, t)$ edges are removed. == Related Problems == Generalizations: Decremental Diameter Related: Median, Radius, Diameter, Diameter 2 vs 3, Diameter 3 vs 7, Approximate Diameter, 1-sen...")
Description
Approximate the diameter of a graph decrementally within a factor of 4/3, with a constant sensitivity of $K(\epsilon, t)$, i.e. when a $K(\epsilon, t)$ edges are removed.
Related Problems
Generalizations: Decremental Diameter
Related: Median, Radius, Diameter, Diameter 2 vs 3, Diameter 3 vs 7, Approximate Diameter, 1-sensitive (4/3)-approximate decremental diameter, 1-sensitive decremental 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 |
|---|---|---|---|---|
| CNF-SAT | assume: SETH then: let $\epsilon > {0}$, $t \in \mathbb{N}$, there exists no algorithm for target with preprocessing time $O(n^t)$, update time $u(n)$ and query time $q(n)$, such that $max\{u(n),q(n)\}=O(n^{1-\epsilon})$ with constant sensitivity $K(\epsilon,t)$ |
2017 | https://arxiv.org/pdf/1703.01638.pdf | link |