메뉴 건너뛰기




Volumn 122, Issue 1-3, 2002, Pages 139-166

Packing equal circles in a square: A deterministic global optimization approach

Author keywords

Branch and bound; Circle packing; Global optimization

Indexed keywords


EID: 84867958818     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(01)00359-6     Document Type: Article
Times cited : (155)

References (22)
  • 1
    • 0000483159 scopus 로고
    • A relaxation method for nonconvex quadratically constrained quadratic programs
    • F.A. Al-Khayyal, C. Larsen, and T. Van Voorhis A relaxation method for nonconvex quadratically constrained quadratic programs J. Global Optim. 6 1995 215 230
    • (1995) J. Global Optim. , vol.6 , pp. 215-230
    • Al-Khayyal, F.A.1    Larsen, C.2    Van Voorhis, T.3
  • 3
    • 20744444485 scopus 로고    scopus 로고
    • Equal circles packing in square II: New results for up to 100 circles using the TAMSASS-PECS algorithm
    • F. Giannessi, P.M. Pardalos, T. Rapcsak (Eds.) Kluwer Academic Publishers, Dordrecht
    • L.G. Casado, I. Garcia, P.G. Szabó, T. Csendes, Equal circles packing in square II: new results for up to 100 circles using the TAMSASS-PECS algorithm, in: F. Giannessi, P.M. Pardalos, T. Rapcsak (Eds.), Optimization Theory: Recent Developments from Mátraháza, Kluwer Academic Publishers, Dordrecht, 2001, pp. 207-224.
    • (2001) Optimization Theory: Recent Developments from Mátraháza , pp. 207-224
    • Casado, L.G.1    Garcia, I.2    Szabó, P.G.3    Csendes, T.4
  • 6
    • 0002367497 scopus 로고
    • The packing of equal circles in a square
    • M. Goldberg The packing of equal circles in a square Math. Mag. 43 1970 24 30
    • (1970) Math. Mag. , vol.43 , pp. 24-30
    • Goldberg, M.1
  • 7
    • 0003504161 scopus 로고    scopus 로고
    • Repeated patterns of dense packings of equal disks in a square
    • R.L. Graham, and B.D. Lubachevsky Repeated patterns of dense packings of equal disks in a square Electron. J. Combin. 3 1996 1 16
    • (1996) Electron. J. Combin. , vol.3 , pp. 1-16
    • Graham, R.L.1    Lubachevsky, B.D.2
  • 9
    • 84861964712 scopus 로고    scopus 로고
    • Packing equal circles in a square: I. Theoretical results
    • Univ. di Firenze
    • M. Locatelli, U. Raber, Packing equal circles in a square: I. Theoretical results, Technical Report 08-99, Dip. Sistemi e Informatica, Univ. di Firenze, 1999, available at the web site http://www.di.unito.it/~locatell/pap1.ps.
    • (1999) Technical Report 08-99, Dip. Sistemi e Informatica
    • Locatelli, M.1    Raber, U.2
  • 10
    • 84867995414 scopus 로고    scopus 로고
    • Packing equal circles in a square: II. A deterministic global optimization approach
    • Univ. di Firenze
    • M. Locatelli, U. Raber, Packing equal circles in a square: II. A deterministic global optimization approach, Technical Report 09-99, Dip. Sistemi e Informatica, Univ. di Firenze, 1999, available at the web site http://www.di.unito.it/~locatell/pap2.ps.
    • (1999) Technical Report 09-99, Dip. Sistemi e Informatica
    • Locatelli, M.1    Raber, U.2
  • 11
    • 0000625923 scopus 로고
    • New results in the packing of equal circles in a square
    • C.D. Maranas, C.A. Floudas, and P.M. Pardalos New results in the packing of equal circles in a square Discrete Math. 142 1995 287 293
    • (1995) Discrete Math. , vol.142 , pp. 287-293
    • Maranas, C.D.1    Floudas, C.A.2    Pardalos, P.M.3
  • 14
    • 0039253425 scopus 로고    scopus 로고
    • More optimal packings of equal circles in a square
    • K.J. Nurmela, and P.R.J. Oestergard More optimal packings of equal circles in a square Discrete Comput. Geom. 22 1999 439 457
    • (1999) Discrete Comput. Geom. , vol.22 , pp. 439-457
    • Nurmela, K.J.1    Oestergard, P.R.J.2
  • 15
    • 0002315226 scopus 로고    scopus 로고
    • A simplicial branch-and-bound method for solving nonconvex all-quadratic programs
    • U. Raber A simplicial branch-and-bound method for solving nonconvex all-quadratic programs J. Global Optim. 13 1998 417 432
    • (1998) J. Global Optim. , vol.13 , pp. 417-432
    • Raber, U.1
  • 17
    • 0039324267 scopus 로고
    • The densest packing of nine circles in a square
    • J. Schaer The densest packing of nine circles in a square Canad. Math. Bull. 8 1965 273 277
    • (1965) Canad. Math. Bull. , vol.8 , pp. 273-277
    • Schaer, J.1
  • 18
    • 0040509551 scopus 로고
    • On a geometric extremum problem
    • J. Schaer, and A. Meir On a geometric extremum problem Canad. Math. Bull. 8 1965 21 27
    • (1965) Canad. Math. Bull. , vol.8 , pp. 21-27
    • Schaer, J.1    Meir, A.2
  • 19
    • 0041103542 scopus 로고
    • Die dichteste packung von 16 kreisen in einem quadrat
    • G. Wengerodt Die dichteste packung von 16 kreisen in einem quadrat Beiträge Algebra Geom. 16 1983 173 190
    • (1983) Beiträge Algebra Geom. , vol.16 , pp. 173-190
    • Wengerodt, G.1
  • 20
    • 0041103543 scopus 로고
    • Die dichteste packung von 14 kreisen in einem quadrat
    • G. Wengerodt Die dichteste packung von 14 kreisen in einem quadrat Beiträge Algebra Geom. 25 1987 25 46
    • (1987) Beiträge Algebra Geom. , vol.25 , pp. 25-46
    • Wengerodt, G.1
  • 22
    • 0041103524 scopus 로고
    • Die dichteste packung von 36 kreisen in einem quadrat
    • G. Wengerodt, and K. Kirchner Die dichteste packung von 36 kreisen in einem quadrat Beiträge Algebra Geom. 25 1987 147 159
    • (1987) Beiträge Algebra Geom. , vol.25 , pp. 147-159
    • Wengerodt, G.1    Kirchner, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.