1 research outputs found
Parameterized algorithms for Partial vertex covers in bipartite graphs
In the weighted partial vertex cover problem (WPVC), we are given a graph
, cost function , profit function , and positive integers and . The goal is to check whether there is a
subset of cost at most , such that the total profit of edges
covered by is at least . In this paper we study the fixed-parameter
tractability of WPVC in bipartite graphs (WPVCB). By extending the methods of
Amini et al., we show that WPVCB is FPT with respect to if . On
the negative side, it is -hard for arbitrary , even when .
In particular, WPVCB is -hard parameterized by . We complement this
negative result by proving that for bounded-degree graphs WPVC is FPT with
respect to . The same result holds for the case of WPVCB when we allow to
take only one fractional vertex. Additionally, we show that WPVC is FPT with
respect to . Finally, we discuss a variant of PVCB in which the edges
covered are constrained to include a matching of prescribed size and derive a
paramterized algorithm for the same.Comment: 12 pages, no figure