Assistance and Interdiction Problems on Interval Graphs
Abstract
We introduce a novel framework of graph modifications specific to interval graphs. We study interdiction problems with respect to these graph modifications. Given a list of original intervals, each interval has a replacement interval such that either the replacement contains the original, or the original contains the replacement. The interdictor is allowed to replace up to original intervals with their replacements. Using this framework we also study the contrary of interdiction problems which we call assistance problems. We study these problems for the independence number, the clique number, shortest paths, and the scattering number. We obtain polynomial time algorithms for most of the studied problems. Via easy reductions, it follows that on interval graphs, the most vital nodes problem with respect to shortest path, independence number and Hamiltonicity can be solved in polynomial time.
Cite
@article{arxiv.2107.14550,
title = {Assistance and Interdiction Problems on Interval Graphs},
author = {Hung P. Hoang and Stefan Lendl and Lasse Wulf},
journal= {arXiv preprint arXiv:2107.14550},
year = {2021}
}