Optimal Parametric Search for Path and Tree Partitioning
Data Structures and Algorithms
2017-11-03 v1
Abstract
We present linear-time algorithms for partitioning a path or a tree with weights on the vertices by removing edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices, removing edges to minimize the maximum-weight component. The algorithms use the parametric search paradigm, testing candidate values until an optimum is found while simultaneously reducing the running time needed for each test. For path-partitioning, the algorithm employs a synthetic weighting scheme that results in a constant fraction reduction in running time after each test. For tree-partitioning, our dual-pronged strategy makes progress no matter what the specific structure of our tree is.
Cite
@article{arxiv.1711.00599,
title = {Optimal Parametric Search for Path and Tree Partitioning},
author = {Greg N. Frederickson and Samson Zhou},
journal= {arXiv preprint arXiv:1711.00599},
year = {2017}
}