| Summary: | 碩士 === 世新大學 === 資訊管理學研究所(含碩專班) === 101 === A hub set of a graph G(V, E) is a subset H of V such that for any two distinct vertices u, v do not belong to H, if (u, v) do not belong to E, then they are connected by a path in H. If <H> is connected, then H is called a connected hub set of G, where <H> represents the subgraph of G induced by the vertices in H. The problem of finding a minimum connected hub set, called the Minimum Connected Hub Set problem (the MCHS problem) is studied in this thesis. We prove that the MCHS problem is NP-hard on split graphs with special constraint and propose linear-time algorithms for on some special graphs. The classes of graphs studied include block-cactus graphs, convex-split graphs, and biconvex-bipartite graphs.
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