iETA #1 Improved Fixed-Parameter Algorithms for Non-Crossing Subgraphs1
نویسندگان
چکیده
We consider the problem of computing non-crossing spanning trees in topological graphs. It is known that it is NP-hard to decide whether a topological graph has a noncrossing spanning tree, and that it is hard to approximate the minimum number of crossings in a spanning tree. We give improved fixed-parameter algorithms, where we use the number k of crossing edge pairs and the number μ of crossing edges in the given graph as parameters. The running times of our algorithms are O∗(kO( √ ) and O∗(μO(μ 2/3)), where the O∗-notation neglects polynomial terms. Our method can be applied to several other non-crossing subgraph problems in topological graphs.
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