On the Parameterized Complexity of Contraction to generalization of trees

Akanksha Agrawal, Saket Saurabh, Prafullkumar Tale

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

For a family of graphs F, the F-Contraction problem takes as an input a graph G and an integer k, and the goal is to decide if there exists S ⊆ E(G) of size at most k such that G/S belongs to F. Here, G/S is the graph obtained from G by contracting all the edges in S. Heggernes et al. [Algorithmica (2014)] were the first to study edge contraction problems in the realm of Parameterized Complexity. They studied F-Contraction when F is a simple family of graphs such as trees and paths. In this paper, we study the F-Contraction problem, where F generalizes the family of trees. In particular, we define this generalization in a "parameterized way". Let T be the family of graphs such that each graph in T can be made into a tree by deleting at most ℓ edges. Thus, the problem we study is T-Contraction. We design an FPT algorithm for T-Contraction running in time O((2√ℓ + 2)O(k+ℓ) · nO(1)). Furthermore, we show that the problem does not admit a polynomial kernel when parameterized by k. Inspired by the negative result for the kernelization, we design a lossy kernel for T-Contraction of size O([k(k + 2ℓ)]([α/α-1]+1)).

Original languageEnglish
Title of host publication12th International Symposium on Parameterized and Exact Computation, IPEC 2017
EditorsDaniel Lokshtanov, Naomi Nishimura
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959770514
DOIs
StatePublished - 1 Feb 2018
Externally publishedYes
Event12th International Symposium on Parameterized and Exact Computation, IPEC 2017 - Vienna, Austria
Duration: 6 Sep 20178 Sep 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume89
ISSN (Print)1868-8969

Conference

Conference12th International Symposium on Parameterized and Exact Computation, IPEC 2017
Country/TerritoryAustria
CityVienna
Period6/09/178/09/17

Keywords

  • Fixed Parameter Tractability
  • Generalization of Trees
  • Graph Algorithms
  • Graph Contraction

ASJC Scopus subject areas

  • Software

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