Continuous bottleneck tree partitioning problems |
| |
Authors: | Nir Halman and Arie Tamir |
| |
Institution: | Department of Statistics and Operations Research, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv 69978, Israel |
| |
Abstract: | We study continuous partitioning problems on tree network spaces whose edges and nodes are points in Euclidean spaces. A continuous partition of this space into p connected components is a collection of p subtrees, such that no pair of them intersect at more than one point, and their union is the tree space. An edge-partition is a continuous partition defined by selecting p−1 cut points along the edges of the underlying tree, which is assumed to have n nodes. These cut points induce a partition into p subtrees (connected components). The objective is to minimize (maximize) the maximum (minimum) “size” of the components (the min–max (max–min) problem). When the size is the length of a subtree, the min–max and the max–min partitioning problems are NP-hard. We present O(n2 log(min(p,n))) algorithms for the edge-partitioning versions of the problem. When the size is the diameter, the min–max problems coincide with the continuous p-center problem. We describe O(n log3 n) and O(n log2 n) algorithms for the max–min partitioning and edge-partitioning problems, respectively, where the size is the diameter of a component. |
| |
Keywords: | Tree partitioning Continuous p-center problems Bottleneck problems Parametric search |
本文献已被 ScienceDirect 等数据库收录! |
|