Slowing down sorting networks to obtain faster sorting algorithms
Journal of the ACM (JACM)
Optimal algorithms for tree partitioning
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Most uniform path partitioning and its use in image processing
Discrete Applied Mathematics - Special issue: combinatorial structures and algorithms
Journal of the ACM (JACM)
A Shifting Algorithm for Min-Max Tree Partitioning
Journal of the ACM (JACM)
Applying Parallel Computation Algorithms in the Design of Serial Algorithms
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A shifting algorithm for continuous tree partitioning
Theoretical Computer Science
New Upper Bounds on Continuous Tree Edge-Partition Problem
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Discrete Applied Mathematics
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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.