The Estimate Of Rigidity Constants Of Circle Packings And Their Hyhrib Particle Swarm Optimization Arithmetic

A circle packing is a configuration of circles with a specified pattern of tangenciesand disjoint interiors. In 1985, Fields prize winner W. Thurston suggested a conjecturethat hexagonal circle packing could be used to approximate Riemann maps. In 1987,B. Rodin and D. Sullivan successfully proved the convergence of scheme. It signed thatthe research on the circle packings had entered into a new developmental times. Hereour main work include two aspects: First, we discuss the approximating estimate of therigidity of bounded degree circle packings. Using the property of bounded degree circlepackings and the relationship between them and conformal mappings, we presented anasymptotic estimate of rigidity constants of bounded degree circle packings, that is,where m denotes the number of edges ofregular polygon. Specially, for m = 4, we have Second, we discuss Hybrid Particle Swarm Optimization arithmetic(HPSO) for circlepackings. The question of finding the circle packing's radius is reduced to the idea ofParticle Swarm Optimization. Then, according to the latter's arithmetic we can ob-tain the former's one. Simulational experiment shows that this kind of Hybrid ParticleSwarm Optimization arithmetic about circle packings is e?ective.