TY - JOUR
T1 - New results in the packing of equal circles in a square
AU - Maranas, Costas D.
AU - Floudas, Christodoulos A.
AU - Pardalos, Panos M.
N1 - Funding Information:
NSF under Grant CTS-
PY - 1995/7/15
Y1 - 1995/7/15
N2 - The problem of finding the maximum diameter of n equal mutually disjoint circles inside a unit square is addressed in this paper. Exact solutions exist for only n = 1, ..., 9,10,16,25,36 while for other n only conjectural solutions have been reported. In this work a max-min optimization approach is introduced which matches the best reported solutions in the literature for all n ≤ 30, yields a better configuration for n = 15, and provides new results for n = 28 and 29.
AB - The problem of finding the maximum diameter of n equal mutually disjoint circles inside a unit square is addressed in this paper. Exact solutions exist for only n = 1, ..., 9,10,16,25,36 while for other n only conjectural solutions have been reported. In this work a max-min optimization approach is introduced which matches the best reported solutions in the literature for all n ≤ 30, yields a better configuration for n = 15, and provides new results for n = 28 and 29.
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U2 - 10.1016/0012-365X(93)E0230-2
DO - 10.1016/0012-365X(93)E0230-2
M3 - Article
AN - SCOPUS:0000625923
SN - 0012-365X
VL - 142
SP - 287
EP - 293
JO - Discrete Mathematics
JF - Discrete Mathematics
IS - 1-3
ER -