We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of "most vital arcs" for flows/paths to geometric environments. We give hardness results and efficient algorithms for various versions of the problem, (almost) completely separating hard and polynomially-solvable cases.
@article{arxiv.1905.01185,
title = {Most vital segment barriers},
author = {Irina Kostitsyna and Maarten Löffler and Valentin Polishchuk and Frank Staals},
journal= {arXiv preprint arXiv:1905.01185},
year = {2019}
}