Approximating the minimum clique cover and other hard problems in subtree filament graphs

Authors:
J. Mark Keil;Lorna Stewart
Affiliations:
Department of Computer Science University of Saskatchewan, Saskatoon, Saskatchewan, Canada;Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada
Venue:
Discrete Applied Mathematics
Year:
2006

Citing 14
Cited 5

Algorithms for maximum k-colorings and k-coverings of transitive graphs

Networks
Linear time algorithms on circular-arc graphs

Information Processing Letters
The complexity of domination problems in circle graphs

Discrete Applied Mathematics
Quantifiers and approximation

Theoretical Computer Science - Special issue on structure in complexity theory
Recognition of circle graphs

Journal of Algorithms
Free Bits, PCPs, and Nonapproximability---Towards Tight Results

SIAM Journal on Computing
Maximum k-Chains in Planar Point Sets: Combinatorial Structure and Algorithms

SIAM Journal on Computing
Label placement by maximum independent set in rectangles

WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
Maximum weight independent sets and cliques in intersection graphs of filaments

Information Processing Letters
Fast stabbing of boxes in high dimensions

Theoretical Computer Science
On the k-Colouring of Circle-Graphs

STACS '88 Proceedings of the 5th Annual Symposium on Theoretical Aspects of Computer Science
The Complexity of Colouring Circle Graphs (Extended Abstract)

STACS '92 Proceedings of the 9th Annual Symposium on Theoretical Aspects of Computer Science
Maximum independent set and maximum clique algorithms for overlap graphs

Discrete Applied Mathematics - Special issue: The second international colloquium, "journées de l'informatique messine"
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Subtree filament graphs are subtree overlap graphs

Information Processing Letters
Minimum weight feedback vertex sets in circle graphs

Information Processing Letters
Parameterized domination in circle graphs

WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
Solving clique covering in very large sparse random graphs by a technique based on k-fixed coloring tabu search

EvoCOP'13 Proceedings of the 13th European conference on Evolutionary Computation in Combinatorial Optimization
Parameterized Domination in Circle Graphs

Theory of Computing Systems

Quantified Score

Hi-index	0.04

Visualization

Abstract

Subtree filament graphs are the intersection graphs of subtree filaments in a tree. This class of graphs contains subtree overlap graphs, interval filament graphs, chordal graphs, circle graphs, circular-arc graphs, cocomparability graphs, and polygon-circle graphs. In this paper we show that, for circle graphs, the clique cover problem is NP-complete and the h-clique cover problem for fixed h is solvable in polynomial time. We then present a general scheme for developing approximation algorithms for subtree filament graphs, and give approximation algorithms developed from the scheme for the following problems which are NP-complete on circle graphs and therefore on subtree filament graphs: clique cover, vertex colouring, maximum k-colourable subgraph, and maximum h-coverable subgraph.