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A Polynomial Kernel for Bipartite Permutation Vertex Deletion

Authors Lawqueen Kanesh, Jayakrishnan Madathil, Abhishek Sahu, Saket Saurabh, Shaily Verma

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Author Details

Lawqueen Kanesh
  • National University of Singapore, Singapore
Jayakrishnan Madathil
  • Chennai Mathematical Institute, Chennai, India
Abhishek Sahu
  • The Institute of Mathematical Sciences, HBNI, Chennai, India
Saket Saurabh
  • The Institute of Mathematical Sciences, HBNI, Chennai, India
  • University of Bergen, Norway
Shaily Verma
  • The Institute of Mathematical Sciences, HBNI, Chennai, India

Funding

  • Kanesh, Lawqueen: Supported in part by NRF Fellowship for AI grant [R-252-000-B14-281] and by Defense Service Organization, Singapore.
  • Madathil, Jayakrishnan: Supported by the Chennai Mathematical Institute and the Infosys Foundation.
  • Saurabh, Saket: Supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 819416), and Swarnajayanti Fellowship (no. DST/SJF/MSA01/2017-18).

Cite AsGet BibTex

Lawqueen Kanesh, Jayakrishnan Madathil, Abhishek Sahu, Saket Saurabh, and Shaily Verma. A Polynomial Kernel for Bipartite Permutation Vertex Deletion. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.IPEC.2021.23

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)}.

Subject Classification

ACM Subject Classification
  • Theory of computation → Fixed parameter tractability
Keywords
  • kernelization
  • bipartite permutation graph
  • bicliques

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