Fixed parameter algorithms for one-sided crossing minimization revisited

Authors:
Vida Dujmović;Henning Fernau;Michael Kaufmann
Affiliations:
Department of Mathematics and Statistics, McGill University, Montréal, Canada;Universität Trier, FB IV, Abt. Informatik, 54286 Trier, Germany;Universität Tübingen, WSI für Informatik, Sand 13, 72076 Tübingen, Germany
Venue:
Journal of Discrete Algorithms
Year:
2008

Citing 7
Cited 4

A general method to speed up fixed-parameter-tractable algorithms

Information Processing Letters
Graph Drawing: Algorithms for the Visualization of Graphs

Graph Drawing: Algorithms for the Visualization of Graphs
One Sided Crossing Minimization Is NP-Hard for Sparse Graphs

GD '01 Revised Papers from the 9th International Symposium on Graph Drawing
An Efficient Fixed Parameter Tractable Algorithm for 1-Sided Crossing Minimization

Algorithmica
An Improved Bound on the One-Sided Minimum Crossing Number in Two-Layered Drawings

Discrete & Computational Geometry
Kernels: annotated, proper and induced

IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Parameterized Complexity

Parameterized Complexity

Comparing trees via crossing minimization

Journal of Computer and System Sciences
Ranking and drawing in subexponential time

IWOCA'10 Proceedings of the 21st international conference on Combinatorial algorithms
An SDP approach to multi-level crossing minimization

Journal of Experimental Algorithmics (JEA)
A fast and simple subexponential fixed parameter algorithm for one-sided crossing minimization

ESA'12 Proceedings of the 20th Annual European conference on Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

We exhibit a small problem kernel for the one-sided crossing minimization problem. This problem plays an important role in graph drawing algorithms based on the Sugiyama layering approach. Moreover, we improve on the search tree algorithm developed in [V. Dujmovic, S. Whitesides, An efficient fixed parameter tractable algorithm for 1-sided crossing minimization, Algorithmica 40 (2004) 15-31] and derive an O(1.4656^k+kn^2) algorithm for this problem, where k upperbounds the number of tolerated edge crossings in the drawings of an n-vertex graph.