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 |
97 |
(7) |
| 9 |
188 |
(8) |
| 10 |
363 |
(8) |
| 11 |
680 |
(1) |
| 12 |
1260 |
(1) |
|
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 |
180 |
(1) |
| 10 |
344 |
(1) |
| 11 |
630 |
(1) |
| 12 |
1238 |
(5) |
|
* denotes absolute bound.
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** Rajan, D.S. and A.M. Shende, "Maximal and Reversible Snakes in
Hypercubes", 24th Annual Australasian Conference on Combinatorial
Mathematics and Combinatorial Computation (1999).
|
|
|
|
**8** 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.
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