Algorithms for graphs embeddable with few crossings per edge

Authors:
Alexander Grigoriev;Hans L. Bodlaender
Affiliations:
Faculty of Economics and Business Administration, Quantitative Economics, Maastricht University, Maastricht, The Netherlands;Institute of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands
Venue:
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
Year:
2005

Citing 9
Cited 2

Approximation algorithms for NP-complete problems on planar graphs

Journal of the ACM (JACM)
Graph theory and its applications

Graph theory and its applications
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
Algorithms for Vertex Partitioning Problems on Partial k-Trees

SIAM Journal on Discrete Mathematics
Local Tree-Width, Excluded Minors, and Approximation Algorithms

Combinatorica
Approximation algorithms for classes of graphs excluding single-crossing graphs as minors

Journal of Computer and System Sciences
Bidimensionality: new connections between FPT algorithms and PTASs

SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Graphs excluding a fixed minor have grids as large as treewidth, with combinatorial and algorithmic applications through bidimensionality

SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A robust PTAS for maximum weight independent sets in unit disk graphs

WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science

Configurations with few crossings in topological graphs

Computational Geometry: Theory and Applications
Acyclic orientation of drawings

SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider graphs that can be embedded on a surface of bounded genus such that each edge has a bounded number of crossings. We prove that many optimization problems, including maximum independent set, minimum vertex cover, minimum dominating set and many others, admit polynomial time approximation schemes when restricted to such graphs. This extends previous results by Baker [1] and Eppstein [7] to a much broader class of graphs.