A list of current records for the Snake-in-the-Box problem (March, 2016).

Dimension | Length | ||
---|---|---|---|

Snakes^{1} | Coils^{2} | Symmetric Coils | |

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*^{[2]} | 26*^{[11]} |

7 | 50*^{[6]} | 48*^{[4]} | 46*^{[12]} |

8 | 98*^{[8,16]} | 96*^{[17]} | 94*^{[9]} |

9 | 190^{[9]} | 188^{[9]} | 186^{[13]} |

10 | 370^{[10]} | 366^{[18]} | 362^{[13]} |

11 | 712^{[18]} | 692^{[18]} | 662^{[13]} |

12 | 1373^{[18]} | 1344^{[18]} | 1222^{[13]} |

13 | 2687^{[18]} | 2594^{[18]} | 2354^{[13]} |

14 | 4932^{[15]} | 4934^{[15]} | |

15 | 9866^{[15]} | 9868^{[15]} |

^{1} Open Snakes (spread 2).
^{2} Closed Snakes (spread 2).
*denotes absolute bound.

- Casella, D.A., and Potter, W.D., "Using Evolutionary Techniques to Hunt for Snakes and Coils", in the
*Proceedings of 2005 IEEE Congress on Evolutionary Computing*, CEC’05, pp 2499-2505, Edinburgh, Scotland, September 2-5, 2005. - Davies, D.W., "Longest -Separated- Paths and Loops in an N Cube",
*IEEE Trans. Electronic Computers*, Vol. 14, p. 261, 1965. - Kautz, W.H., "Unit-Distance Error-Checking Codes",
*IRE Trans. Electronic Computers*, Vol. 7, pp 179-180, 1958. - Kochut, K.J., "Snake-in-the-box codes for dimension 7",
*J Comb Math Comb Comput*, Vol. 20, pp 175-185, 1996. - Paterson, K.G. and Tuliani, J., "Some New Circuit Codes",
*IEEE Transactions on Information Theory*, Vol. 44(3), pp 1305-1309, 1998. - Potter, W.D., Robinson R.W., Miller J.A., and Kochut, K.J., "Using the Genetic Algorithm to Find Snake- In-The-Box Codes", In
*Proceeding of the 7th International Conference on Industrial & Engineering Applications of Artificial Intelligence and Expert Systems*, pp 421-426. Austin, Texas, 1994. - Tuohy D.R., Potter, W.D., and Casella, D.A., "Searching for snake-in-the-box codes with evolved pruning models", In: Arabnia HR, Yang JY, Yang MQ (eds)
*Proc 2007 Int Conf Genet and Evol Methods*(GEM’2007). CSREA Press, pp 3-9, 2007. - Carlson, B.P., and Hougen D., "Phenotype Feedback Genetic Algorithm Operators for Heuristic Encoding of Snakes and Hypercubes", in the
*Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation*, GECCO '10, pp 791-798, Portland, Oregon, USA, July 07 - 11, 2010. - Wynn, E., “Personal Communications”, (11/2009, dim 9 186), 8/2010, 1/13/2012. See also "Constructing Circuit Codes by Permuting Initial Sequences".
- Kinny, D., “A New Approach to the Snake-In-The-Box-Problem”,
*Proceeding of ECAI 2012*, doi:10.3233/978-1-61499-098-7.462. - Adelson, L.E., Alter, R.,and Curtz, T.B., "Long snakes and a characterization of maximal snakes on the d-cube", in the
*Proceedings of 4th SouthEastern Conference on Combinatorics, Graph Theory and Computing*, Congr. Numer. 8, pp 111-124, 1973. - 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. - Meyerson, S., Whiteside, W., Drapela, T., and Potter, W.D., “Finding Longest Paths in Hypercubes: Snakes and Coils,” in
*Proceedings of the IEEE Symposium on Computational Intelligence for Engineering Solutions*, IEEE CIES'14, pp. 103-109, Orlando, FL, December, 2014; and “Finding Longest Paths in Hypercubes, 11 New Lower Bounds: Snake, Coils, and Symmetric Coils,” in the*Proceedings of the 28th Industrial, Engineering and Other Applications of Applied Intelligent Systems*, LNAI-9101: Current Approaches in Applied Artificial Intelligence, Springer International, pp. 23-32. - Kinny, D., “Monte-Carlo Search for Snakes and Coils”,
*Proceedings of the Sixth International Workshop*, MIWAI'2012, LNCS-7694: Multi-Disciplinary Trends in Artificial Intelligence, pp. 271-283. - Abbott, H., and Katchalski, M., “On The Construction of Snake In The Box Codes,”
*Utilitas Mathematica*, 40, 97-116, 1991. - Ostergard, P.R.J., and Pettersson, V.H., “Exhaustive Search for Snake-in-the-Box Codes”,
*Graphs and Combinatorics*, May, 2014. - Ostergard, P.R.J., and Pettersson, V.H., “On the Maximum Length of Coil-in-the-Box Codes in Dimension 8”,
*Discrete Applied Mathematics*, 179, pp. 193-200, 2014. - Allison, D., and Paulusma, D., “New Bounds for the Snake-in-the-Box Problem”, (arXiv.org/abs/1603.05119), March, June, 2016.