Geometric Separation and Exact Solutions for the Parameterized Independent Set Problem on Disk Graphs [chapter]

Jochen Alber, Jiří Fiala
2002 Foundations of Information Technology in the Era of Network and Mobile Computing  
We consider the parameterized problem, whether for a given set D of n disks (of bounded radius ratio) in the Euclidean plane there exists a set of k non-intersecting disks. We expose an algorithm running in time n O( √ k) , that is-to our knowledge-the first algorithm for this problem with running time bounded by an exponential with a sublinear exponent. For λ-precision disk graphs of bounded radius ratio, we show that the problem is fixed parameter tractable with respect to parameter k. The
more » ... ults are based on a new "geometric √ ·-separator theorem" which holds for all disk graphs of bounded radius ratio. 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. Our techniques can be extended to various other graph problems, such as dominating set, to obtain similar results for disk graphs of bounded radius ratio.
doi:10.1007/978-0-387-35608-2_3 dblp:conf/ifipTCS/AlberF02 fatcat:uwl6jfili5avvhw5x6wfswrimy