Interdiction Problems on Planar Graphs

TL;DR

This paper studies interdiction problems on planar graphs, providing approximation algorithms for some cases and proving strong NP-completeness for others, advancing understanding of computational complexity in network interdiction.

Contribution

Introduces approximation algorithms and NP-completeness results for interdiction problems on planar graphs, including the first planar NP-completeness proof for budget-constrained flow improvement.

Findings

A $(1 + psilon)$-approximation algorithm for maximum matching interdiction on weighted planar graphs.

Proves several interdiction problems are strongly NP-complete on planar graphs.

First planar NP-completeness proof using a one-vertex crossing gadget.

Abstract

Interdiction problems are leader-follower games in which the leader is allowed to delete a certain number of edges from the graph in order to maximally impede the follower, who is trying to solve an optimization problem on the impeded graph. We introduce approximation algorithms and strong NP-completeness results for interdiction problems on planar graphs. We give a multiplicative $(1 + \epsilon)$-approximation for the maximum matching interdiction problem on weighted planar graphs. The algorithm runs in pseudo-polynomial time for each fixed $\epsilon > 0$. We also show that weighted maximum matching interdiction, budget-constrained flow improvement, directed shortest path interdiction, and minimum perfect matching interdiction are strongly NP-complete on planar graphs. To our knowledge, our budget-constrained flow improvement result is the first planar NP-completeness proof that uses a one-vertex crossing gadget.