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Volumn 52, Issue 4, 2012, Pages 855-868

Packing congruent hyperspheres into a hypersphere

Author keywords

Hexagonal lattice; Hypersphere; Mathematical model; Optimization; Packing

Indexed keywords

FEASIBLE DIRECTION METHODS; GLOBAL MAXIMUM; HEXAGONAL LATTICE; HYPERSPHERE; LATTICE PACKINGS; LOCAL MAXIMUM; NUMERICAL RESULTS; SOLUTION APPROACH;

EID: 84875653446     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-011-9716-z     Document Type: Article
Times cited : (24)

References (21)
  • 3
    • 36448976929 scopus 로고    scopus 로고
    • Minimizing the object dimensions in circle and sphere packing problems
    • 10.1016/j.cor.2006.11.002
    • Birgin E.G.; Sobral F.N.C.: Minimizing the object dimensions in circle and sphere packing problems. Comput. Oper. Res. 35, 2357-2375 (2008)
    • (2008) Comput. Oper. Res. , vol.35 , pp. 2357-2375
    • Birgin, E.G.1    Sobral, F.N.C.2
  • 5
    • 0029358316 scopus 로고
    • HOPDM (version 2.12): A fast LP solver based on a primal-dual interior point method
    • 10.1016/0377-2217(95)00163-K
    • Gondzio J.: HOPDM (version 2.12): A fast LP solver based on a primal-dual interior point method. Eur. J. Oper. Res. 85(1), 221-225 (1995)
    • (1995) Eur. J. Oper. Res. , vol.85 , Issue.1 , pp. 221-225
    • Gondzio, J.1
  • 6
  • 7
    • 22044441063 scopus 로고    scopus 로고
    • A proof of the Kepler conjecture
    • 10.4007/annals.2005.162.65
    • Hales T.C.: A proof of the Kepler conjecture. Ann. Math 162(1), 065-1185 (2005)
    • (2005) Ann. Math , vol.162 , Issue.1 , pp. 065-1185
    • Hales, T.C.1
  • 8
    • 78751537817 scopus 로고    scopus 로고
    • A literature review on circle and sphere packing problems: Models and methodologies
    • Hifi, M.; M'Hallah, R.: A literature review on circle and sphere packing problems: models and methodologies. Adv. Oper. Res. (2009)
    • (2009) Adv. Oper. Res.
    • Hifi, M.1    M'Hallah, R.2
  • 9
    • 84886725203 scopus 로고    scopus 로고
    • Modeling languages in optimization a new paradigm
    • C.A. Floudas M. Pardalos (eds) 2 Springer New York 10.1007/978-0-387- 74759-0-399
    • Hürlimann T.: Modeling languages in optimization a new paradigm. In: Floudas, C.A.; Pardalos, P.M. (eds) Encyclopedia of Optimization, 2nd Edn.; pp. 2297-2304. Springer, New York (2009)
    • (2009) Encyclopedia of Optimization , pp. 2297-2304
    • Hürlimann, T.1
  • 10
    • 59549087550 scopus 로고    scopus 로고
    • Cutting circles and polygons from area-minimizing rectangles
    • 10.1007/s10898-007-9274-6
    • Kallrath J.: Cutting circles and polygons from area-minimizing rectangles. J. Glob. Optim 43, 299-328 (2009)
    • (2009) J. Glob. Optim , vol.43 , pp. 299-328
    • Kallrath, J.1
  • 11
    • 0009408686 scopus 로고
    • Complexity of packing, covering, and partitioning problems
    • Schrijver, A. (ed.) Mathematisch Centrum, Amsterdam
    • Lenstra, J.K.; Rinnooy, A.H.G.: Complexity of packing, covering, and partitioning problems. In: Schrijver, A. (ed.) Packing and Covering in Combinatorics, pp. 275-291. Mathematisch Centrum, Amsterdam (1979)
    • (1979) Packing and Covering in Combinatorics , pp. 275-291
    • Lenstra J., .K.1    Rinnooy A. .H., .G.2
  • 12
    • 0000625923 scopus 로고
    • New results in the packing of equal circles in a square
    • 10.1016/0012-365X(93)E0230-2
    • Maranas C.D.; Floudas C.A.; Pardalos P.M.: New results in the packing of equal circles in a square. Discret. Math. 142(1-3), 287-293 (1995)
    • (1995) Discret. Math. , vol.142 , Issue.1-3 , pp. 287-293
    • Maranas, C.D.1    Floudas, C.A.2    Pardalos, P.M.3
  • 13
    • 70350640918 scopus 로고    scopus 로고
    • An effective hybrid algorithm for the circles and spheres packing problems
    • D.-Z. Du X. Hu M. Pardalos (eds) Springer New York
    • Liu J. et al.: An effective hybrid algorithm for the circles and spheres packing problems. In: Du, D.-Z.; Hu, X.; Pardalos, P.M. (eds) COCOA 2009, LNCS, vol. 5573, pp. 135-144. Springer, New York (2009)
    • (2009) COCOA 2009, LNCS, Vol. 5573 , pp. 135-144
    • Liu, J.1
  • 14
    • 33750548448 scopus 로고    scopus 로고
    • Packing hyperspheres in high-dimensional Euclidean spaces
    • 10.1103/PhysRevE.74.041127
    • Skoge M.; Donev A.; Stillinger F.H.; Torquato S.: Packing hyperspheres in high-dimensional Euclidean spaces. Phys. Rev. E 74, 041127 (2006)
    • (2006) Phys. Rev. e , vol.74 , pp. 041127
    • Skoge, M.1    Donev, A.2    Stillinger, F.H.3    Torquato, S.4
  • 15
    • 60649096867 scopus 로고    scopus 로고
    • Packing cylinders and rectangular parallelepipeds with distances between them into a given region
    • 10.1016/j.ejor.2008.07.003
    • Stoyan Y.; Chugay A.: Packing cylinders and rectangular parallelepipeds with distances between them into a given region. Eur. J. Oper. Res. 197, 446-455 (2009)
    • (2009) Eur. J. Oper. Res. , vol.197 , pp. 446-455
    • Stoyan, Y.1    Chugay, A.2
  • 16
    • 79958168093 scopus 로고    scopus 로고
    • Packing identical spheres into a rectangular parallelepiped
    • A. Bortfeldt J. Homberger H. Kopfer G. Pankratz R. Strangmeier (eds) Verlag Dr. Th. Gabler GWV Fachverlage GmbH
    • Stoyan Y.; Yaskov G.: Packing identical spheres into a rectangular parallelepiped. In: Bortfeldt, A.; Homberger, J.; Kopfer, H.; Pankratz, G.; Strangmeier, R. (eds) Intelligent Decision Support Current Challenges and Approaches, Wiesbaden: Betriebswirtschaftlicher, pp. 46-67. Verlag Dr. Th. Gabler, GWV Fachverlage GmbH (2008)
    • (2008) Intelligent Decision Support Current Challenges and Approaches, Wiesbaden: Betriebswirtschaftlicher , pp. 46-67
    • Stoyan, Y.1    Yaskov, G.2
  • 17
    • 21144437792 scopus 로고    scopus 로고
    • A polyhedral branch-and-cut approach to global optimization
    • 10.1007/s10107-005-0581-8
    • Tawarmalani M.; Sahinidis N.V.: A polyhedral branch-and-cut approach to global optimization. Math. Program. 103(2), 225-249 (2005)
    • (2005) Math. Program. , vol.103 , Issue.2 , pp. 225-249
    • Tawarmalani, M.1    Sahinidis, N.V.2
  • 18
    • 33644883967 scopus 로고    scopus 로고
    • Exactly solvable disordered sphere-packing model in arbitrary-dimensional Euclidean spaces
    • 10.1103/PhysRevE.73.031106
    • Torquato S.: Exactly solvable disordered sphere-packing model in arbitrary-dimensional Euclidean spaces. Phys. Rev. E 73, 031106 (2006)
    • (2006) Phys. Rev. e , vol.73 , pp. 031106
    • Torquato, S.1
  • 19
    • 0012717006 scopus 로고
    • Über einem geometrischen Satz
    • 10.1007/BF01181430 (In German)
    • Toth L.F.: Über einem geometrischen Satz. Mathematische Zeitschrift 46, 83-85 (1940) (In German)
    • (1940) Mathematische Zeitschrift , vol.46 , pp. 83-85
    • Toth, L.F.1
  • 21
    • 84886724997 scopus 로고    scopus 로고
    • http://hydra.nat.uni-magdeburg.de/packing/cci/cci.html


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.