Geometric Separator for d-Dimensional Ball Graphs
نویسندگان
چکیده
We study the graph partitioning problem on ddimensional ball graphs in a geometric way. Let B be a set of balls in d-dimensional Euclidean space with radius ratio δ and λ-precision. We prove that it can be partitioned into three sets BS , BI , BE such that the intersection of BI and BE is empty, and for some constant α, the volume of BI and BE is less than α portion of volume of B, and the volume of BS is of size O(σ/λ, (μ(B)) 1 d ), where μ(B) is the volume of B. We also provide a randomized algorithm to find such a partition in linear time.
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