9,391 research outputs found
A QPTAS for the Base of the Number of Triangulations of a Planar Point Set
The number of triangulations of a planar n point set is known to be ,
where the base lies between and The fastest known algorithm
for counting triangulations of a planar n point set runs in time.
The fastest known arbitrarily close approximation algorithm for the base of the
number of triangulations of a planar n point set runs in time subexponential in
We present the first quasi-polynomial approximation scheme for the base of
the number of triangulations of a planar point set
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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