Packing of unitary-radius circles in a rectangle (minimizing perimeter)

Number of items Length Width Item-item
Overlap		 Item-object
Overlap		 Solution Files Number of trials CPU time in seconds
1 2.0000000000000000 2.0000000000000000 0.0E+00 0.0E+00 IMAGE cr-minp-1.dat cr-minp-1.mp 1 0.00
2 4.0000000000000000 2.0000000000000000 0.0E+00 0.0E+00 IMAGE cr-minp-2.dat cr-minp-2.mp 1 0.00
3 3.7320508075688776 4.0000000000000000 0.0E+00 0.0E+00 IMAGE cr-minp-3.dat cr-minp-3.mp 2 0.00
4 4.0000000000000000 4.0000000000000000 0.0E+00 0.0E+00 IMAGE cr-minp-4.dat cr-minp-4.mp 3 0.17
5 4.0000000000000000 5.4641016151377544 6.7E-16 0.0E+00 IMAGE cr-minp-5.dat cr-minp-5.mp 6 0.24
6 4.0000000000000000 6.0000000000000000 0.0E+00 0.0E+00 IMAGE cr-minp-6.dat cr-minp-6.mp 3 0.32
7 5.8612097182041998 5.4641016151377553 0.0E+00 0.0E+00 IMAGE cr-minp-7.dat cr-minp-7.mp 26 1.06
8 5.4641016151377553 6.0000000000000009 0.0E+00 0.0E+00 IMAGE cr-minp-8.dat cr-minp-8.mp 11 1.50
9 6.0000000000000000 6.0000000000000000 0.0E+00 0.0E+00 IMAGE cr-minp-9.dat cr-minp-9.mp 2 0.01
10 7.1961524227066338 6.0000000000000009 0.0E+00 0.0E+00 IMAGE cr-minp-10.dat cr-minp-10.mp 390 44.93
11 6.0000000000000009 7.4641016151377562 0.0E+00 0.0E+00 IMAGE cr-minp-11.dat cr-minp-11.mp 18 3.62
12 6.0000000000000000 8.0000000000000000 0.0E+00 0.0E+00 IMAGE cr-minp-12.dat cr-minp-12.mp 18 3.79
13 7.4626564857803901 7.4632672693142670 0.0E+00 0.0E+00 IMAGE cr-minp-13.dat cr-minp-13.mp 15222 1944.55
14 7.1961524227066338 8.0000000000000018 0.0E+00 0.0E+00 IMAGE cr-minp-14.dat cr-minp-14.mp 223 42.44
15 8.0000000000000018 7.4641016151377562 0.0E+00 0.0E+00 IMAGE cr-minp-15.dat cr-minp-15.mp 78 14.93
16 8.0000000000000000 8.0000000000000000 0.0E+00 0.0E+00 IMAGE cr-minp-16.dat cr-minp-16.mp 108 24.32
17 8.9282032302755123 7.9427193491449888 4.4E-16 0.0E+00 IMAGE cr-minp-17.dat cr-minp-17.mp 3240 737.93
18 8.0000000000000036 8.9282032302755123 4.4E-16 0.0E+00 IMAGE cr-minp-18.dat cr-minp-18.mp 1089 287.59
19 7.4641016151377562 10.0000000000000018 0.0E+00 0.0E+00 IMAGE cr-minp-19.dat cr-minp-19.mp 17 7.37
20 8.9282032302755123 9.0000000000000036 4.4E-16 0.0E+00 IMAGE cr-minp-20.dat cr-minp-20.mp 1758 556.65
21 9.4337452285295686 9.2209018981307658 0.0E+00 0.0E+00 IMAGE cr-minp-21.dat cr-minp-21.mp 351 113.34
22 9.9427193491449888 8.9282032302755123 4.4E-16 0.0E+00 IMAGE cr-minp-22.dat cr-minp-22.mp 3141 979.18
23 8.9282032302755123 10.0000000000000036 4.4E-16 0.0E+00 IMAGE cr-minp-23.dat cr-minp-23.mp 1127 421.24
24 9.4641016151377553 10.0000000000000000 0.0E+00 0.0E+00 IMAGE cr-minp-24.dat cr-minp-24.mp 207 86.33
25 11.0000000000000036 8.9282032302755123 4.4E-16 0.0E+00 IMAGE cr-minp-25.dat cr-minp-25.mp 541 213.47
26 10.6602540378443891 9.9427193491449888 4.4E-16 0.0E+00 IMAGE cr-minp-26.dat cr-minp-26.mp 9147 3528.82
27 10.6602540378443891 10.0000000000000036 4.4E-16 0.0E+00 IMAGE cr-minp-27.dat cr-minp-27.mp 184 88.10
28 12.0000000000000036 8.9282032302755123 4.4E-16 0.0E+00 IMAGE cr-minp-28.dat cr-minp-28.mp 191 74.90
29 9.4641016151377571 12.0000000000000018 0.0E+00 0.0E+00 IMAGE cr-minp-29.dat cr-minp-29.mp 32 20.58
30 10.6602540378443891 11.0000000000000036 4.4E-16 0.0E+00 IMAGE cr-minp-30.dat cr-minp-30.mp 792 436.24
31 10.9282032302755141 11.4265717909344140 4.4E-16 0.0E+00 IMAGE cr-minp-31.dat cr-minp-31.mp 4023 2237.26
32 11.9427193491449870 10.6602540378443891 1.3E-15 0.0E+00 IMAGE cr-minp-32.dat cr-minp-32.mp 2624 1417.69
33 12.0000000000000036 10.6602540378443891 4.4E-16 0.0E+00 IMAGE cr-minp-33.dat cr-minp-33.mp 328 214.35
34 10.9282032302755123 12.0000000000000036 4.4E-16 0.0E+00 IMAGE cr-minp-34.dat cr-minp-34.mp 1081 731.71
35 12.3923048454132676 11.0000000000000036 4.4E-16 0.0E+00 IMAGE cr-minp-35.dat cr-minp-35.mp 176 133.13
36 10.6602540378443891 13.0000000000000071 4.4E-16 0.0E+00 IMAGE cr-minp-36.dat cr-minp-36.mp 146 82.16
37 12.3923048454132676 11.8612097182042024 4.4E-16 0.0E+00 IMAGE cr-minp-37.dat cr-minp-37.mp 11245 7399.74
38 11.9841557353269081 12.3924132707237522 -8.9E-16 0.0E+00 IMAGE cr-minp-38.dat cr-minp-38.mp 4365 2891.91
39 12.3923048454132676 12.0000000000000036 4.4E-16 0.0E+00 IMAGE cr-minp-39.dat cr-minp-39.mp 4844 3329.17
40 12.9282032302755123 12.0000000000000036 4.4E-16 0.0E+00 IMAGE cr-minp-40.dat cr-minp-40.mp 176 155.32
41 12.3923048454132676 12.9427193491449888 4.4E-16 0.0E+00 IMAGE cr-minp-41.dat cr-minp-41.mp 7353 6254.69
42 12.3923048454132676 13.0000000000000071 4.4E-16 0.0E+00 IMAGE cr-minp-42.dat cr-minp-42.mp 1879 1650.45
43 13.6029140930960750 12.3923268915991969 2.2E-16 0.0E+00 IMAGE cr-minp-43.dat cr-minp-43.mp 1035 1035.43
44 13.8844501917489893 12.3923048454132712 4.4E-16 0.0E+00 IMAGE cr-minp-44.dat cr-minp-44.mp 14400 13131.52
45 13.9841229965638760 12.3923048454132676 4.4E-16 0.0E+00 IMAGE cr-minp-45.dat cr-minp-45.mp 921 1069.14
46 14.0000000000000071 12.6602540378443891 4.4E-16 0.0E+00 IMAGE cr-minp-46.dat cr-minp-46.mp 1529 1879.21
47 14.0000000000000071 12.9282032302755123 4.4E-16 0.0E+00 IMAGE cr-minp-47.dat cr-minp-47.mp 1149 1281.24
48 13.0000000000000071 14.1243556529821479 4.4E-16 0.0E+00 IMAGE cr-minp-48.dat cr-minp-48.mp 1400 1709.87
49 12.3923048454132676 15.0000000000000071 4.4E-16 0.0E+00 IMAGE cr-minp-49.dat cr-minp-49.mp 5969 7546.82
50 12.3923048454132712 15.6028097181778964 4.4E-16 0.0E+00 IMAGE cr-minp-50.dat cr-minp-50.mp 4730 6366.25