Polynomial Kernels and Faster Algorithms for the Dominating Set Problem on Graphs with an Excluded Minor
نویسنده
چکیده
The domination number of a graph G = (V,E) is the minimum size of a dominating set U ⊆ V , which satisfies that every vertex in V \U is adjacent to at least one vertex in U . The notion of a problem kernel refers to a polynomial time algorithm that achieves some provable reduction of the input size. Given a graph G whose domination number is k, the objective is to design a polynomial time algorithm that produces a graph G whose size depends only on k, and also has domination number equal to k. Note that the graph G is constructed without knowing the value of k. Problem kernels can be used to obtain efficient approximation and exact algorithms for the domination number, and are also useful in
منابع مشابه
Linear kernels for (connected) dominating set on graphs with excluded topological subgraphs
We give the first linear kernels for Dominating Set and Connected Dominating Set problems on graphs excluding a fixed graph H as a topological minor. In other words, we give polynomial time algorithms that, for a given H-topological-minor free graph G and a positive integer k, output an H-topological-minor free graph G′ on O(k) vertices such that G has a (connected) dominating set of size k if ...
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