Kanesh, Lawqueen ;
Madathil, Jayakrishnan ;
Sahu, Abhishek ;
Saurabh, Saket ;
Verma, Shaily
A Polynomial Kernel for Bipartite Permutation Vertex Deletion
Abstract
In a permutation graph, vertices represent the elements of a permutation, and edges represent pairs of elements that are reversed by the permutation. In the Permutation Vertex Deletion problem, given an undirected graph G and an integer k, the objective is to test whether there exists a vertex subset S ⊆ V(G) such that S ≤ k and GS is a permutation graph. The parameterized complexity of Permutation Vertex Deletion is a wellknown open problem. Bożyk et al. [IPEC 2020] initiated a study towards this problem by requiring that GS be a bipartite permutation graph (a permutation graph that is bipartite). They called this the Bipartite Permutation Vertex Deletion (BPVD) problem. They showed that the problem admits a factor 9approximation algorithm as well as a fixed parameter tractable (FPT) algorithm running in time 𝒪(9^k V(G)⁹). And they posed the question {whether BPVD admits a polynomial kernel.}
We resolve this question in the affirmative by designing a polynomial kernel for BPVD. In particular, we obtain the following: Given an instance (G,k) of BPVD, in polynomial time we obtain an equivalent instance (G',k') of BPVD such that k' ≤ k, and V(G')+E(G') ≤ k^{𝒪(1)}.
BibTeX  Entry
@InProceedings{kanesh_et_al:LIPIcs.IPEC.2021.23,
author = {Kanesh, Lawqueen and Madathil, Jayakrishnan and Sahu, Abhishek and Saurabh, Saket and Verma, Shaily},
title = {{A Polynomial Kernel for Bipartite Permutation Vertex Deletion}},
booktitle = {16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
pages = {23:123:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783959772167},
ISSN = {18688969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl  LeibnizZentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/15406},
URN = {urn:nbn:de:0030drops154065},
doi = {10.4230/LIPIcs.IPEC.2021.23},
annote = {Keywords: kernelization, bipartite permutation graph, bicliques}
}
22.11.2021
Keywords: 

kernelization, bipartite permutation graph, bicliques 
Seminar: 

16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Issue date: 

2021 
Date of publication: 

22.11.2021 