Affiliation:
1. Royal Holloway, University of London, Egham Hill, Egham, UK
Abstract
We show the existence of an exact mimicking network of
k
O
(
log
k
) edges for minimum multicuts over a set of terminals in an undirected graph, where
k
is the total capacity of the terminals, i.e., the sum of the degrees of the terminal vertices. Furthermore, using the best available approximation algorithm for
Small Set Expansion
, we show that a mimicking network of
k
O
(
log3
k
) edges can be computed in randomized polynomial time. As a consequence, we show quasipolynomial kernels for several problems, including
Edge Multiway Cut
,
Group Feedback Edge Set
for an arbitrary group, and
Edge Multicut
parameterized by the solution size and the number of cut requests. The result combines the matroid-based irrelevant edge approach used in the kernel for
s
-Multiway Cut
with a recursive decomposition and sparsification of the graph along sparse cuts. This is the first progress on the kernelization of
Multiway Cut
problems since the kernel for
s
-Multiway Cut
for constant value of
s
(Kratsch and Wahlström, FOCS 2012).
Publisher
Association for Computing Machinery (ACM)
Subject
Mathematics (miscellaneous)