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Balanced Crown Decomposition for Connectivity Constraints

Authors Katrin Casel , Tobias Friedrich , Davis Issac , Aikaterini Niklanovits , Ziena Zeif

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Katrin Casel
  • Hasso Plattner Institute, University of Potsdam, Germany
Tobias Friedrich
  • Hasso Plattner Institute, University of Potsdam, Germany
Davis Issac
  • Hasso Plattner Institute, University of Potsdam, Germany
Aikaterini Niklanovits
  • Hasso Plattner Institute, University of Potsdam, Germany
Ziena Zeif
  • Hasso Plattner Institute, University of Potsdam, Germany

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Katrin Casel, Tobias Friedrich, Davis Issac, Aikaterini Niklanovits, and Ziena Zeif. Balanced Crown Decomposition for Connectivity Constraints. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.ESA.2021.26

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 approximation algorithms and kernelization 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 k 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
Keywords
  • crown decomposition
  • connected partition
  • balanced partition
  • approximation algorithms

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