Partitioning algorithms for weighted trees and cactus graphs
Abstract
In this paper, we consider different constrained partition problems for weighted trees and cactus graphs. We focus on the (l,u)-partition problem, which is the problem of partitioning a weighted graph into connected clusters such that each cluster fulfills the lower and upper weight constraints l and u. Partitioning into a minimum, maximum or a fixed number of clusters is known to be NP-hard in general, but polynomial-time solvable on trees. We prove that these three variants of the (l,u)-partition problem can be solved for cactus graphs as well by presenting a polynomial-time algorithm. Additionally, we present an efficient method to compute the corresponding partitions. For other optimization goals or additional constraints, the partition problem becomes NP-hard - even on trees and for a lower weight bound equal to zero. We show that our method can be used as an algorithmic framework to solve other partition problems for weighted trees and cactus graphs with a pseudopolynomial runtime.
Cite
@article{arxiv.2001.00204,
title = {Partitioning algorithms for weighted trees and cactus graphs},
author = {Maike Buchin and Leonie Selbach},
journal= {arXiv preprint arXiv:2001.00204},
year = {2022}
}