Balanced Crown Decomposition for Connectivity Constraints
Abstract
We introduce the balanced crown decomposition that captures the structure imposed on graphs by their connected induced subgraphs of a given size. Such subgraphs are a popular modeling tool in various application areas, where the non-local nature of the connectivity condition usually results in very challenging algorithmic tasks. The balanced crown decomposition is a combination of a crown decomposition and a balanced partition which makes it applicable to graph editing as well as graph packing and partitioning problems. We illustrate this by deriving improved kernelization and approximation algorithms for a variety of such problems. In particular, through this structure, we obtain the first constant-factor approximation for the Balanced Connected Partition (BCP) problem, where the task is to partition a vertex-weighted graph into connected components of approximately equal weight. We derive a 3-approximation for the two most commonly used objectives of maximizing the weight of the lightest component or minimizing the weight of the heaviest component.
Keywords
Cite
@article{arxiv.2011.04528,
title = {Balanced Crown Decomposition for Connectivity Constraints},
author = {Katrin Casel and Tobias Friedrich and Davis Issac and Aikaterini Niklanovits and Ziena Zeif},
journal= {arXiv preprint arXiv:2011.04528},
year = {2021}
}