Computing the cutwidth of bipartite permutation graphs in linear time

Authors:
Pinar Heggernes;Pim Van 't Hof;Daniel Lokshtanov;Jesper Nederlof
Affiliations:
Department of Informatics, University of Bergen, Bergen, Norway;School of Engineering and Computing Sciences, Durham University, Science Laboratories, Durham, United Kingdom;Department of Informatics, University of Bergen, Bergen, Norway;Department of Informatics, University of Bergen, Bergen, Norway
Venue:
WG'10 Proceedings of the 36th international conference on Graph-theoretic concepts in computer science
Year:
2010

Citing 16
Cited 1

A polynomial algorithm for the min-cut linear arrangement of trees

Journal of the ACM (JACM)
Min Cut is NP-complete for edge weighted trees

International Colloquium on Automata, Languages and Programming on Automata, languages and programming
A randomized fully polynomial time approximation scheme for the all terminal network reliability problem

STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Graph classes: a survey

Graph classes: a survey
Approximating layout problems on random geometric graphs

Journal of Algorithms
A survey of graph layout problems

ACM Computing Surveys (CSUR)
Minimizing Width in Linear Layouts

Proceedings of the 10th Colloquium on Automata, Languages and Programming
A Polyhedral Approach to Planar Augmentation and Related Problems

ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
A new rounding procedure for the assignment problem with applications to dense graph arrangement problems

FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Polynomial time algorithms for the MIN CUT problem on degree restricted trees

SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
An approximate max-flow min-cut theorem for uniform multicommodity flow problems with applications to approximation algorithms

SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Cutwidth of Split Graphs, Threshold Graphs, and Proper Interval Graphs

Graph-Theoretic Concepts in Computer Science
Bipartite permutation graphs

Discrete Applied Mathematics
Cutwidth I: A linear time fixed parameter algorithm

Journal of Algorithms
Cutwidth II: Algorithms for partial w-trees of bounded degree

Journal of Algorithms
Fixed-parameter algorithms for protein similarity search under mRnA structure constraints

WG'05 Proceedings of the 31st international conference on Graph-Theoretic Concepts in Computer Science

On cutwidth parameterized by vertex cover

IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation

Quantified Score

Hi-index	0.00

Visualization

Abstract

The problem of determining the cutwidth of a graph is a notoriously hard problem which remains NP-complete under severe restrictions on input graphs. Until recently, non-trivial polynomial-time cutwidth algorithms were known only for subclasses of graphs of bounded treewidth. In WG 2008, Heggernes et al. initiated the study of cutwidth on graph classes containing graphs of unbounded treewidth, and showed that a greedy algorithm computes the cutwidth of threshold graphs. We continue this line of research and present the first polynomial-time algorithm for computing the cutwidth of bipartite permutation graphs. Our algorithm runs in linear time. We stress that the cutwidth problem is NP-complete on bipartite graphs and its computational complexity is open even on small subclasses of permutation graphs, such as trivially perfect graphs.