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Interdiction Problems on Planar Graphs
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 -approximation for the maximum matching
interdiction problem on weighted planar graphs. The algorithm runs in
pseudo-polynomial time for each fixed . 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.Comment: 25 pages, 9 figures. Extended abstract in APPROX-RANDOM 201
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