We propose models for lobbying in a probabilistic environment, in which an actor (called The Lobby) seeks to influence voters preferences of voting for or against multiple issues when the voters preferences are represented in terms of probabilities.
In particular, we provide two evaluation criteria and two bribery methods to formally describe these models, and we consider the resulting forms of lobbying with and without issue weighting. We provide a formal analysis for these problems of lobbying in a stochastic environment, and determine their classical and parameterized complexity depending on the given bribery/evaluation criteria and on various natural parameterizations. Specifically, we show that some of these problems can be solved in polynomial time, some are NP-complete but fixed-parameter tractable, and some are W[2]-complete. Finally, we provide approximability and inapproximability results for these problems and several variants.
}We study (vertex-disjoint) $P_2$-packings in graphs under a parameterized perspective. Starting from a maximal $P_2$-packing $p$ of size $j$ we use extremal arguments for determining how many vertices of $p$ appear in some $P_2$-packing of size $(j+
1)$. We basically can reuse $2.5j$ vertices. We also present a kernelization algorithm that gives a kernel of size bounded by $7k$. With these two results we build an algorithm which constructs a $P_2$-packing of size $k$ in time $Oh^*(2.482^{3k})$.
