Simulated annealing: theory and applications
Simulated annealing: theory and applications
On the thickness of graphs of given degree
Information Sciences: an International Journal
On the thickness and arboricity of a graph
Journal of Combinatorial Theory Series B
An O(m log n)-time algorithm for the maximal planar subgraph problem
SIAM Journal on Computing
Modern heuristic techniques for combinatorial problems
Modern heuristic techniques for combinatorial problems
On heuristics for determining the thickness of a graph
Information Sciences—Informatics and Computer Science: An International Journal
Journal of the ACM (JACM)
A genetic algorithm for determining the thickness of a graph
Information Sciences—Informatics and Computer Science: An International Journal
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
Worst case analysis of a greedy algorithm for graph thickness
Information Processing Letters
Information Sciences—Informatics and Computer Science: An International Journal
Remarks on the thickness and outerthickness of a graph
Computers & Mathematics with Applications
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The thickness of a graph is the minimum number of planar subgraphs into which the graph can be decomposed. Determining the thickness of a given graph is known to be an NP-complete problem.In this paper we introduce a new heuristic algorithm for determining the thickness of a graph. Our algorithm is based on the simulated annealing optimization scheme. We compare the quality of the solutions and running times of our algorithm against previously tested heuristic algorithms. We show that the simulated annealing is a fast and efficient method to obtain good approximations for the thickness of a graph.We also give a new upper bound for the thickness of complete tripartite graphs, whose vertex sets are of equal size.