  The voter process is a classic stochastic process that models the invasion of
a mutant trait $A$ (e.g., a new opinion, belief, legend, genetic mutation,
magnetic spin) in a population of agents (e.g., people, genes, particles) who
share a resident trait $B$, spread over the nodes of a graph. An agent may
adopt the trait of one of its neighbors at any time, while the invasion bias
$r\in(0,\infty)$ quantifies the stochastic preference towards ($r>1$) or
against ($r<1$) adopting $A$ over $B$. Success is measured in terms of the
fixation probability, i.e., the probability that eventually all agents have
adopted the mutant trait $A$. In this paper we study the problem of fixation
probability maximization under this model: given a budget $k$, find a set of
$k$ agents to initiate the invasion that maximizes the fixation probability. We
show that the problem is NP-hard for both $r>1$ and $r<1$, while the latter
case is also inapproximable within any multiplicative factor. On the positive
side, we show that when $r>1$, the optimization function is submodular and thus
can be greedily approximated within a factor $1-1/e$. An experimental
evaluation of some proposed heuristics corroborates our results.
