Agrawal, Akanksha ;
Saurabh, Saket ;
Tale, Prafullkumar
On the Parameterized Complexity of Contraction to Generalization of Trees
Abstract
For a family of graphs F, the FContraction problem takes as an input a graph G and an integer k, and the goal is to decide if there exists S \subseteq 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 \cal FContraction when F is a simple family of graphs such as trees and paths. In this paper, we study the FContraction problem, where F generalizes the family of trees. In particular, we define this generalization in a "parameterized way". Let T_\ell be the family of graphs such that each graph in T_\ell can be made into a tree by deleting at most \ell edges. Thus, the problem we study is T_\ellContraction. We design an FPT algorithm for T_\ellContraction running in time O((\ncol)^{O(k + \ell)} * n^{O(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_\ellContraction of size O([k(k + 2\ell)] ^{(\lceil {\frac{\alpha}{\alpha1}\rceil + 1)}}).
BibTeX  Entry
@InProceedings{agrawal_et_al:LIPIcs:2018:8544,
author = {Akanksha Agrawal and Saket Saurabh and Prafullkumar Tale},
title = {{On the Parameterized Complexity of Contraction to Generalization of Trees}},
booktitle = {12th International Symposium on Parameterized and Exact Computation (IPEC 2017)},
pages = {1:11:12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959770514},
ISSN = {18688969},
year = {2018},
volume = {89},
editor = {Daniel Lokshtanov and Naomi Nishimura},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/8544},
URN = {urn:nbn:de:0030drops85446},
doi = {10.4230/LIPIcs.IPEC.2017.1},
annote = {Keywords: Graph Contraction, Fixed Parameter Tractability, Graph Algorithms, Generalization of Trees}
}
02.03.2018
Keywords: 

Graph Contraction, Fixed Parameter Tractability, Graph Algorithms, Generalization of Trees 
Seminar: 

12th International Symposium on Parameterized and Exact Computation (IPEC 2017)

Issue date: 

2018 
Date of publication: 

02.03.2018 