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On Approximate Compressions for Connected Minor-Hitting Sets

Author M. S. Ramanujan

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M. S. Ramanujan
  • University of Warwick, Coventry, UK

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M. S. Ramanujan. On Approximate Compressions for Connected Minor-Hitting Sets. In 29th Annual European Symposium on Algorithms (ESA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 204, pp. 78:1-78:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ESA.2021.78

Abstract

In the Connected ℱ-Deletion problem, ℱ is a fixed finite family of graphs and the objective is to compute a minimum set of vertices (or a vertex set of size at most k for some given k) such that (a) this set induces a connected subgraph of the given graph and (b) deleting this set results in a graph which excludes every F ∈ ℱ as a minor. In the area of kernelization, this problem is well known to exclude a polynomial kernel subject to standard complexity hypotheses even in very special cases such as ℱ = K₂, i.e., Connected Vertex Cover.
In this work, we give a (2+ε)-approximate polynomial compression for the Connected ℱ-Deletion problem when ℱ contains at least one planar graph. This is the first approximate polynomial compression result for this generic problem. As a corollary, we obtain the first approximate polynomial compression result for the special case of Connected η-Treewidth Deletion.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Mathematics of computing → Approximation algorithms
Keywords
  • Parameterized Complexity
  • Kernelization
  • Approximation Algorithms

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