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DOI: 10.4230/LIPIcs.IPEC.2021.23
URN: urn:nbn:de:0030-drops-154065
URL: https://drops.dagstuhl.de/opus/volltexte/2021/15406/
Kanesh, Lawqueen ; Madathil, Jayakrishnan ; Sahu, Abhishek ; Saurabh, Saket ; Verma, Shaily
A Polynomial Kernel for Bipartite Permutation Vertex Deletion
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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 G-S is a permutation graph. The parameterized complexity of Permutation Vertex Deletion is a well-known open problem. Bożyk et al. [IPEC 2020] initiated a study towards this problem by requiring that G-S 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 9-approximation 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 = {23:1--23:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-216-7},
ISSN = {1868-8969},
year = {2021},
volume = {214},
editor = {Golovach, Petr A. and Zehavi, Meirav},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/15406},
URN = {urn:nbn:de:0030-drops-154065},
doi = {10.4230/LIPIcs.IPEC.2021.23},
annote = {Keywords: kernelization, bipartite permutation graph, bicliques}
}
| 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 |
