A optimization algorithm for determining the thickness of complete graphs and complete bipartite graphs


Abstract in English

The graph-theoretical thickness (shortly thickness)of graph G, denoted by Φ(G), is the minimum number of planar subgraphs into which the graph can be decomposed, and a graph that can be drawn in the plane without any of its edges intersecting is called a planar graph. determining the thickness of a given graph is known to be an NP-complete problem. In this paper we introduce an application heuristic algorithm for determining the thickness. Our algorithm is based on simulated annealing optimization scheme which provide the results of the New-thick (1). We show that the simulated annealing is a efficient method to obtain good approximation for the thickness when the number vertices are at most 30 otherwise it is slower. Finally, we apply this algorithm on the heuristic algorithm Newthick and we show that the algorithm produces a good approximation and optimization solution for the thickness, and we program this algorithm with C++, and running it by laptop has RAM 2GB and CPU 2.27GHZ.

References used

BONDY, J and MURTY, U. S 2008-Graph Theory . Springer
artrand,G 1993-Applied and Algorithmic Graph Theory. McGraw-Hill,Inc, International Edition United States of America, 395
Daniel Liang,Y 2010-Introduction to Programming With C++. Pearson Education International, second edition United States of America, 694
Eles, P 2010- Simulated Annealing.Department of Computer and Information Science (IDA)Linköpings Universitet
JOHN,M. MICHAEL,J and JEFFRY,L 2008-Combinatorics and Graph Theory, second edition Springer, 392

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