000			a
999			_c29759 _d29759
008			191121b xxu||||| |||| 00| 0 eng d
020			_a9780387456737
082			_a516​.11 _bSZA
100			_aSzabo, P. G.
245			_aNew approaches to circle packing in a square : with program codes
260			_aBoston _bSpringer _c2007
300			_axiv, 238 p. _bill. _c24 cm. _e1 CD-ROM _g4 3/​4 in.
365			_b109.99 _cEUR _d82.00
490			_aSpringer optimization and its applications _vv. 6
504			_aIncludes bibliography and index.
520			_aIn one sense, the problem of finding the densest packing of congruent circles in a square is easy to understand: it is a matter of positioning a given number of equal circles in such a way that the circles fit fully in a square without overlapping. But on closer inspection, this problem reveals itself to be an interesting challenge of discrete and computational geometry with all its surprising structural forms and regularities. As the number of circles to be packed increases, solving a circle packing problem rapidly becomes rather difficult. To give an example of the difficulty of some problems, consider that in several cases there even exists a circle in an optimal packing that can be moved slightly while retaining the optimality. Such free circles (or "rattles") mean that there exist not only a continuum of optimal solutions, but the measure of the set of optimal solutions is positive! This book summarizes results achieved in solving the circle packing problem over the past few years, providing the reader with a comprehensive view of both theoretical and computational achievements. Typically illustrations of problem solutions are shown, elegantly displaying the results obtained. Beyond the theoretically challenging character of the problem, the solution methods developed in the book also have many practical applications. Direct applications include cutting out congruent two-dimensional objects from an expensive material, or locating points within a square in such a way that the shortest distance between them is maximal. Circle packing problems are closely related to the "obnoxious facility location" problems, to the Tammes problem, and less closely related to the Kissing Number Problem. The emerging computational algorithms can also be helpful in other hard-to-solve optimization problems like molecule conformation. The wider scientific community has already been involved in checking the codes and has helped in having the computational proofs accepted. Since the codes can be worked with directly, they will enable the reader to improve on them and solve problem instances that still remain challenging, or to use them as a starting point for solving related application problems. AudienceThis book will appeal to those interested in discrete geometrical problems and their efficient solution techniques. Operations research and optimization experts will also find it worth reading as a case study of how the utilization of the problem structure and specialities made it possible to find verified solutions of previously hopeless high-dimensional nonlinear optimization problems with nonlinear constraints.
650			_aMathematical Optimization
650			_aConvex and Discrete Geometry
650			_aArithmetic and Logic Structures
650			_aMath Applications in Computer Science
700			_aMarkot, M. Cs.
700			_aCsendes, T.
700			_aSpecht, E.
700			_aCasado, L. G.
700			_aGarcia, I.
942			_2ddc _cBK