1 research outputs found
Improved Region-Growing and Combinatorial Algorithms for -Route Cut Problems
We study the {\em -route} generalizations of various cut problems, the
most general of which is \emph{-route multicut} (-MC) problem, wherein we
have source-sink pairs and the goal is to delete a minimum-cost set of
edges to reduce the edge-connectivity of every source-sink pair to below .
The -route extensions of multiway cut (-MWC), and the minimum - cut
problem (--cut), are similarly defined. We present various
approximation and hardness results for these -route cut problems that
improve the state-of-the-art for these problems in several cases. (i) For {\em
-route multiway cut}, we devise simple, but surprisingly effective,
combinatorial algorithms that yield bicriteria approximation guarantees that
markedly improve upon the previous-best guarantees. (ii) For {\em -route
multicut}, we design algorithms that improve upon the previous-best
approximation factors by roughly an -factor, when , and
for general and unit costs and any fixed violation of the connectivity
threshold . The main technical innovation is the definition of a new,
powerful \emph{region growing} lemma that allows us to perform region-growing
in a recursive fashion even though the LP solution yields a {\em different
metric} for each source-sink pair. (iii) We complement these results by showing
that the {\em -route - cut} problem is at least as hard to approximate
as the {\em densest--subgraph} (DkS) problem on uniform hypergraphs