Complexity and algorithms for constant diameter augmentation problems

TL;DR

This paper investigates the computational complexity of transforming a graph into one with a specified diameter using a limited number of edge deletions, providing insights for different diameter values.

Contribution

It determines the complexity of constant diameter augmentation problems for various diameter values, advancing understanding of graph modification challenges.

Findings

Complexity results vary depending on the target diameter.

Certain cases are proven to be NP-hard.

Some diameter values admit polynomial-time solutions.

Abstract

We study the following problem: for given integers $d,k$ and graph $G$, can we obtain a graph with diameter $d$ via at most $k$ edge deletions ? We determine the computational complexity of this and related problems for different values of $d$.