Matches in DBpedia 2015-10 for { ?s ?p "In computational geometry, a maximum disjoint set (MDS) is a largest set of non-overlapping geometric shapes selected from a given set of candidate shapes.Finding an MDS is important in applications such as automatic label placement, VLSI circuit design, and cellular frequency division multiplexing.Every set of non-overlapping shapes is an independent set in the intersection graph of the shapes. Therefore, the MDS problem is a special case of the maximum independent set (MIS) problem. Both problems are NP complete, but finding a MDS may be easier than finding a MIS in two respects: For the general MIS problem, the best known exact algorithms are exponential. In some geometric intersection graphs, there are sub-exponential algorithms for finding a MDS. The general MIS problem is hard to approximate and doesn't even have a constant-factor approximation. In some geometric intersection graphs, there are polynomial-time approximation schemes (PTAS) for finding a MDS.The MDS problem can be generalized by assigning a different weight to each shape and searching for a disjoint set with a maximum total weight.In the following text, MDS(C) denotes the maximum disjoint set in a set C."@en }
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- Maximum_disjoint_set abstract "In computational geometry, a maximum disjoint set (MDS) is a largest set of non-overlapping geometric shapes selected from a given set of candidate shapes.Finding an MDS is important in applications such as automatic label placement, VLSI circuit design, and cellular frequency division multiplexing.Every set of non-overlapping shapes is an independent set in the intersection graph of the shapes. Therefore, the MDS problem is a special case of the maximum independent set (MIS) problem. Both problems are NP complete, but finding a MDS may be easier than finding a MIS in two respects: For the general MIS problem, the best known exact algorithms are exponential. In some geometric intersection graphs, there are sub-exponential algorithms for finding a MDS. The general MIS problem is hard to approximate and doesn't even have a constant-factor approximation. In some geometric intersection graphs, there are polynomial-time approximation schemes (PTAS) for finding a MDS.The MDS problem can be generalized by assigning a different weight to each shape and searching for a disjoint set with a maximum total weight.In the following text, MDS(C) denotes the maximum disjoint set in a set C.".