Given a graph G, an integer kβ₯0, and a non-negative integral function
f:V(G)βN, the {\sc Vector Domination} problem asks
whether a set S of vertices, of cardinality k or less, exists in G so
that every vertex vβV(G)βS has at least f(v) neighbors in S. The
problem generalizes several domination problems and it has also been shown to
generalize Bounded-Degree Vertex Deletion. In this paper, the parameterized
version of Vector Domination is studied when the input graph is planar. A
linear problem kernel is presented