Vertex Deletion into Bipartite Permutation Graphs

A permutation graph can be defined as an intersection graph of segments whose endpoints lie on two parallel lines ℓ 1 and ℓ 2 , one on each. A bipartite permutation graph is a permutation graph which is bipartite. In this paper we study the parameterized complexity of the bipartite permutation verte...

Full description

Saved in:
Bibliographic Details
Published in:Algorithmica Vol. 84; no. 8; pp. 2271 - 2291
Main Authors: Bożyk, Łukasz, Derbisz, Jan, Krawczyk, Tomasz, Novotná, Jana, Okrasa, Karolina
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2022
Springer Nature B.V
Subjects:
Algorithm Analysis and Problem Complexity
Algorithms
Apexes
Computer Science
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Deletion
Graph theory
Graphs
Mathematics of Computing
Permutations
Polynomials
Special Issue: Parameterized and Exact Computation (IPEC 2020)
Theory of Computation
Graph modification problems
Partially ordered set
Permutation graphs
Comparability graphs
ISSN:0178-4617, 1432-0541
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A permutation graph can be defined as an intersection graph of segments whose endpoints lie on two parallel lines ℓ 1 and ℓ 2 , one on each. A bipartite permutation graph is a permutation graph which is bipartite. In this paper we study the parameterized complexity of the bipartite permutation vertex deletion problem, which asks, for a given n -vertex graph, whether we can remove at most k vertices to obtain a bipartite permutation graph. This problem is NP -complete by the classical result of Lewis and Yannakakis [ 20 ]. We analyze the structure of the so-called almost bipartite permutation graphs which may contain holes (large induced cycles) in contrast to bipartite permutation graphs. We exploit the structural properties of the shortest hole in a such graph. We use it to obtain an algorithm for the bipartite permutation vertex deletion problem with running time O ( 9 k · n 9 ) , and also give a polynomial-time 9-approximation algorithm.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
content type line 23
ISSN:0178-4617
1432-0541
DOI:10.1007/s00453-021-00923-7