2,292 research outputs found
On the NP-Completeness of the Perfect Perfect Matching Free Subgraph Problem
Given a bipartite graph G = (U υ V,E) such that |U| = |V | and every edge is labelled true or false or both, the perfect matching free subgraph problem is to determine whether or not there exists a subgraph of G containing, for each node u of U, either all the edges labelled true or all the edges labelled false incident to u, and which does not contain a perfect matching. This problem arises in the structural analysis of differential-algebraic systems. The purpose of this paper is to show that this problem is NP-complete. We show that the problem is equivalent to the stable set problem in a restricted case of tripartite graphs. Then we show that the latter remains NP-complete in that case. We also prove the NP-completeness of the related minimum blocker problem in bipartite graphs with perfect matching
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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