English

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 kk edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices, removing kk 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.

Keywords

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}
}
R2 v1 2026-06-22T22:33:41.458Z