Abstract

We introduce approximation algorithms and strong NP-completeness results for 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 give a multiplicative (1 + ε)-approximation algorithm for the weighted maximum matching interdiction problem on weighted planar graphs. The algorithm runs in pseudo-polynomial time for each fixed ε > 0. We also show that weighted maximum matching interdiction remains strongly NP-complete on planar graphs. In the process, we show that the budget-constrained flow improvement, directed shortest path interdiction, and minimum perfect matching interdiction problems 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.

Keywords

maximum matching maximum flow interdiction planar graphs crossing gadget approximation scheme 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Feng Pan
    • 1
  • Aaron Schild
    • 2
  1. 1.D-6, Los Alamos National LaboratoryUSA
  2. 2.Princeton UniversityUSA

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