Records
Latest Records for the Snake-in-the-Box Problem (January, 2012)
Dimensions |
Snakes1 |
Coils2 |
Symmetric Coils |
|||
Length |
Source |
Length |
Source |
Length |
Source |
|
| 1 | 1* | - | 0* | - | 0* | - |
| 2 | 2* | (2) | 4* | (3) | 4* | (11) |
| 3 | 4* | (2) | 6* | (3) | 6* | (11) |
| 4 | 7* | (2) | 8* | (3) | 8* | (11) |
| 5 | 13* | (2) | 14* | (3) | 14* | (11) |
| 6 | 26* | (2) | 26* | (3) | 26* | (11) |
| 7 | 50* | (6) | 48* | (4) | 46* | (12) |
| 8 | 98 | (8) | 96 | (5) | 94 | (9) |
| 9 | 190++ | (9) | 188 ++ | (9) | 170 | (9) |
| 10 | 367++ | (10) | 348 ++ | (9) | 294 | (9) |
| 11 | 689++ | (10) | 640 ++ | (9) | 494 | (9) |
| 12 | 1265++ | (10) | 1238 | (5) | 902 | (9) |
1 Open Snakes.
2 Closed Snakes.
* 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. and Hougen, D., "Phenotype Feedback Genetic Algorithm Operators for Heuristic Encoding of Snakes within Hypercubes", Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, 791-798 (2010).
**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
updated 13/1/2012.