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Volumn 37, Issue 1-4 SPEC. ISS., 2004, Pages 253-261

Optimal packing of 28 equal circles in a unit square - The first reliable solution

Author keywords

branch and bound methods; circle packing; interval arithmetic

Indexed keywords


EID: 10044250325     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:NUMA.0000049472.75023.0a     Document Type: Conference Paper
Times cited : (15)

References (17)
  • 1
    • 0008457383 scopus 로고
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    • C. de Groot M. Monagan, R. Peikert and D. Würtz, Packing circles in a square: Review and new results, in: System Modeling and Optimization - Proc. of the 15th IFIP Conf., ed. P. Kall, Zürich, 1991, Lecture Notes in Control and Information Services, Vol. 180 (Springer, 1992) pp. 45-54.
    • (1992) Lecture Notes in Control and Information Services , vol.180 , pp. 45-54
    • De Groot, C.1    Monagan, M.2    Peikert, R.3    Würtz, D.4
  • 2
    • 0039324272 scopus 로고
    • The optimal packing of ten equal circles in a square
    • ETH, Zürich
    • C. de Groot, R. Peikert and D. Würtz, The optimal packing of ten equal circles in a square, IPS Research Report 90-12, ETH, Zürich (1990).
    • (1990) IPS Research Report , vol.90 , Issue.12
    • De Groot, C.1    Peikert, R.2    Würtz, D.3
  • 3
    • 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. Combinatorics 3(R16) (1996).
    • (1996) Electron. J. Combinatorics , vol.3 , Issue.R16
    • Graham, R.L.1    Lubachevsky, B.D.2
  • 5
    • 84862482205 scopus 로고    scopus 로고
    • http://www.packomania.com, updated by E. Specht.
    • Specht, E.1
  • 8
    • 84867958818 scopus 로고    scopus 로고
    • Packing equal circles in a square: A deterministic global optimization approach
    • M. Locatelli and U. Raber, Packing equal circles in a square: A deterministic global optimization approach, Discrete Appl. Math. 122 (2002) 139-166.
    • (2002) Discrete Appl. Math. , vol.122 , pp. 139-166
    • Locatelli, M.1    Raber, U.2
  • 9
    • 10044292820 scopus 로고    scopus 로고
    • An interval method to validate optimal solutions of the "Packing circles in a unit square" problems
    • M.Cs. Markót, An interval method to validate optimal solutions of the "Packing circles in a unit square" problems, CEJOR 8 (2000) 63-78.
    • (2000) CEJOR , vol.8 , pp. 63-78
    • Markót, M.Cs.1
  • 10
    • 0012758721 scopus 로고    scopus 로고
    • Multisection in interval branch-and-bound methods for global optimization II. Numerical tests
    • M.Cs. Markót, T. Csendes and A.E. Csallner, Multisection in interval branch-and-bound methods for global optimization II. Numerical tests, J. Global Optim. 16 (2000) 219-228.
    • (2000) J. Global Optim. , vol.16 , pp. 219-228
    • Markót, M.Cs.1    Csendes, T.2    Csallner, A.E.3
  • 12
    • 0004293209 scopus 로고
    • Prentice-Hall, Englewood Cliffs, NJ
    • R.E. Moore, Interval Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1966).
    • (1966) Interval Analysis
    • Moore, R.E.1
  • 15
    • 0002125682 scopus 로고
    • Dichteste Packungen von gleichen Kreisen in einem Quadrat
    • R. Peikert, Dichteste Packungen von gleichen Kreisen in einem Quadrat, Elemente der Mathematik 49 (1994) 17-25.
    • (1994) Elemente der Mathematik , vol.49 , pp. 17-25
    • Peikert, R.1
  • 17
    • 10044227084 scopus 로고    scopus 로고
    • Some new structures for the "Equal circles packing in a square" problem
    • P.G. Szabó, Some new structures for the "Equal circles packing in a square" problem, CEJOR 8 (2000) 79-91.
    • (2000) CEJOR , vol.8 , pp. 79-91
    • Szabó, P.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.