Geometric Separation and Exact Solutions for the Parameterized Independent Set Problem on Disk Graphs
نویسندگان
چکیده
We consider the parameterized problem, whether a given set of n disks (of bounded radius) in the Euclidean plane contains k non-intersecting disks. We expose an algorithm running in time n √ , that is—to our knowledge—the first algorithm for this problem with running time bounded by an exponential with a sublinear exponent. The results are based on a new “geometric √ ·-separator theorem” which holds for all disk graphs of bounded radius. The presented algorithm then performs, in a first step, a “geometric problem kernelization” and, in a second step, uses divide-and-conquer based on our geometric separator theorem.
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