Optimal Cuts and Partitions in Tree Metrics in Polynomial Time
Data Structures and Algorithms
2012-12-17 v1 Computational Complexity
Discrete Mathematics
Combinatorics
Optimization and Control
Abstract
We present a polynomial time dynamic programming algorithm for optimal partitions in the shortest path metric induced by a tree. This resolves, among other things, the exact complexity status of the optimal partition problems in one dimensional geometric metric settings. Our method of solution could be also of independent interest in other applications. We discuss also an extension of our method to the class of metrics induced by the bounded treewidth graphs.
Keywords
Cite
@article{arxiv.1212.3471,
title = {Optimal Cuts and Partitions in Tree Metrics in Polynomial Time},
author = {Marek Karpinski and Andrzej Lingas and Dzmitry Sledneu},
journal= {arXiv preprint arXiv:1212.3471},
year = {2012}
}