Snakes (aka: open snakes)
Dimension
|
Length
|
Source
|
| 1 |
1* |
- |
| 2 |
2* |
(2) |
| 3 |
4* |
(2) |
| 4 |
7* |
(2) |
| 5 |
13* |
(2) |
| 6 |
26* |
(2) |
| 7 |
50* |
(6) |
| 8 |
98 |
(8) |
| 9 |
190 ++ |
(9) |
| 10 |
367++ |
(10) |
| 11 |
689++ |
(10) |
| 12 |
1265++ |
(10) |
|
Coils (aka: closed snakes)
Dimension
|
Length
|
Source
|
| 1 |
0* |
- |
| 2 |
4* |
(3) |
| 3 |
6* |
(3) |
| 4 |
8* |
(3) |
| 5 |
14* |
(3) |
| 6 |
26* |
(3) |
| 7 |
48* |
(4) |
| 8 |
96 |
(5) |
| 9 |
188 ++ |
(9) |
| 10 |
348 ++ |
(9) |
| 11 |
640 ++ |
(9) |
| 12 |
1238 |
(5) |
|
Symmetric Coils
Dimension
|
Length
|
Source
|
| 1 |
0* |
- |
| 2 |
4* |
(11) |
| 3 |
6* |
(11) |
| 4 |
8* |
(11) |
| 5 |
14* |
(11) |
| 6 |
26* |
(11) |
| 7 |
46* |
(12) |
| 8 |
94 |
(9) |
| 9 |
170 |
(9) |
| 10 |
294 |
(9) |
| 11 |
494 |
(9) |
| 12 |
902 |
(9) |
* denotes absolute bound.
++ NEW.
References:
| **1** Casella, D.A. and W.D. Potter, "Using Evolutionary Techniques
to Hunt for Snakes and Coils". Proceedings of the 2005 IEEE
Congress on Evolutionary Computing , Edinburgh, Scotland, September,
2005. |
|
| **2** Davies, D.W., "Longest 'separated' paths and loops in an
N-cube", IEEE Trans. Electron. Comput EC-14 (1965) 261.
|
|
| **3** Kautz, W.H., "Unit-Distance Error-Checking Codes",
IRE Transactions on Electronic Computers, Vol EC-7, (1958) 179-180. |
|
| **4** Kochut, K.J., "Snake-in-the-Box Codes for Dimension 7.",
Journal of Combinatorial Mathematics and Combinatorial Computing 20
(1998) 175--185. |
|
| **5** Paterson, K.G. and J. Tuliani, "Some New Circuit Codes",
IEEE Transactions on Information Theory, Vol. 44, No. 3, 1305-1309
(1998). |
|
| **6** Potter, W.D., R.W. Robinson, J.A. Miller and K.J. Kochut, "Using
the Genetic Algorithm to find Snake-in-the-Box Codes", Proceedings
of the 7th International Conference on Industrial & Engineering
Applications of Artificial Intelligence and Expert Systems (1994)
307-314. |
|
|
| **7** Tuohy, D.R., W.D. Potter and D.A. Casella, "Searching for
Snake-in-the-Box Codes with Evolved Pruning Models", Proceedings
of the 2007 Int. Conf. on Genetic and Evolutionary Methods (GEM'2007),
3-9. |
|
| **8** Carlson, B.P., "personal communications". |
|
| **9** Wynn, E., "personal communications", (11/2009, dim 9 186), 8/2010, 1/13/2012. |
|
| **10** Kinny, David, 11/1/2011 Details Forthcoming. |
| **11** Adelson, L.E., Alter, R., and Curtz, T.B., "Long Snakes and a Characterization of Maximal Snakes in the d-Cube", in the Proceedings of 4th SouthEastern Conference on Combinatorics, Graph Theory and Computing, Congr. Number 8, pp 111-124,1973
|
| **12** Adelson, L.E., Alter, R., and Curtz, T.B., "Computation of
d-Dimensional Snakes", in the Proceedings
of 4th SouthEastern Conference on Combinatorics, Graph Theory and Computing, Congr. Number 8, pp 135-139,1973
|
| **13** Potter, W.D., current experimental result |
|
