eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-12
5:1
5:15
10.4230/LIPIcs.SWAT.2020.5
article
Vertex Downgrading to Minimize Connectivity
Aissi, Hassene
1
Chen, Da Qi
2
Ravi, R.
3
Paris Dauphine University, France
Carnegie Mellon University, Pittsburgh, PA, USA
Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA, USA
We consider the problem of interdicting a directed graph by deleting nodes with the goal of minimizing the local edge connectivity of the remaining graph from a given source to a sink. We introduce and study a general downgrading variant of the interdiction problem where the capacity of an arc is a function of the subset of its endpoints that are downgraded, and the goal is to minimize the downgraded capacity of a minimum source-sink cut subject to a node downgrading budget. This models the case when both ends of an arc must be downgraded to remove it, for example. For this generalization, we provide a bicriteria (4,4)-approximation that downgrades nodes with total weight at most 4 times the budget and provides a solution where the downgraded connectivity from the source to the sink is at most 4 times that in an optimal solution. We accomplish this with an LP relaxation and rounding using a ball-growing algorithm based on the LP values. We further generalize the downgrading problem to one where each vertex can be downgraded to one of k levels, and the arc capacities are functions of the pairs of levels to which its ends are downgraded. We generalize our LP rounding to get a (4k,4k)-approximation for this case.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol162-swat2020/LIPIcs.SWAT.2020.5/LIPIcs.SWAT.2020.5.pdf
Vertex Interdiction
Vertex Downgrading
Network Interdiction
Approximation Algorithm