4 research outputs found
Two-sets cut-uncut on planar graphs
We study the following Two-Sets Cut-Uncut problem on planar graphs. Therein,
one is given an undirected planar graph and two sets of vertices and
. The question is, what is the minimum number of edges to remove from ,
such that we separate all of from all of , while maintaining that every
vertex in , and respectively in , stays in the same connected component.
We show that this problem can be solved in time with a
one-sided error randomized algorithm. Our algorithm implies a polynomial-time
algorithm for the network diversion problem on planar graphs, which resolves an
open question from the literature. More generally, we show that Two-Sets
Cut-Uncut remains fixed-parameter tractable even when parameterized by the
number of faces in the plane graph covering the terminals , by
providing an algorithm of running time .Comment: 22 pages, 5 figure