| Summary: | 碩士 === 國立東華大學 === 資訊工程學系 === 95 === A Roman dominating function on a graph G = (V, E) is a function f : V → f(0, 1, 2) satisfying that every vertex u with f(u) = 0 has a neighbor v with f(v) = 2. The weight of the Roman dominating function f is the sum of f(v) for the vertices belonging to V. The Roman domination number of a graph G is the minimum weight of all possible Roman dominating functions on G.
The motivation of Roman domination is in assigning the minimum armies to protect all castles and villages at the age of Roman Empire. If two armies locate in an area, they can protect the area that they located and those areas that are their neighborhood. If an area is assigned an army, the army can protect only the place that they located. In this thesis, we consider the Roman domination problem on graphs of bounded treewidth.
By using a nice tree decomposition T of the input graph G, our algorithm works from leaves to the root of T. Since the treewidth of G is bounded, the time for computing the information of each node of T is constant. Thus, we obtain a linear-time algorithm for the Roman domination problem on bounded treewidth graphs.
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