Diameter -- the task of computing the length of a longest shortest path -- is a fundamental graph problem. Assuming the Strong Exponential Time Hypothesis, there is no O(n1.99)-time algorithm even in sparse graphs [Roditty and Williams, 2013]. To circumvent this lower bound we aim for algorithms with running time f(k)(n+m) where k is a parameter and f is a function as small as possible. We investigate which parameters allow for such running times. To this end, we systematically explore a hierarchy of structural graph parameters.
@article{arxiv.1802.10048,
title = {Parameterized Complexity of Diameter},
author = {Matthias Bentert and André Nichterlein},
journal= {arXiv preprint arXiv:1802.10048},
year = {2020}
}