Threshold Dominating Sets and an Improved Characterization of W[2]
نویسندگان
چکیده
The Threshold Dominating Set problem is that of determining for a graph G = (V, E) whether there is a subset V ′ ⊆ V of size k, such that for each vertex v ∈ V there are at least r elements of the closed neighborhood N [v] that belong to V ′. We consider the complexity of the problem parameterized by the pair (k, r). It is trivial to observe that this is hard for W [2]. It can also be easily shown to belong to a natural extension W ∗[2] of W [2] defined in terms of circuit families of depth bounded by a function of the parameter. We prove membership in W [2] and thus W [2]-completeness. Using this as a starting point, we prove that W ∗[2] = W [2].
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عنوان ژورنال:
- Theor. Comput. Sci.
دوره 209 شماره
صفحات -
تاریخ انتشار 1998