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A list of current records for the Snake-in-the-Box problem (July, 2014).

Dimension Length
Snakes1 Coils2 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*[3] 26*[11]
7 50*[6] 48*[4] 46*[12]
8 98[8] 96[5] 94[9]
9 190[9] 188[9] 186[13]
10 370[10] 358[13] 362[13]
11 707[13] 668[13] 662[13]
12 1302[13] 1276[13] 1222[13]
13 2520[13] 2468[15] 2354[13]

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

References

  1. 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.
  2. Davies, D.W., "Longest -Separated- Paths and Loops in an N Cube", IEEE Trans. Electronic Computers, Vol. 14, p. 261, 1965.
  3. Kautz, W.H., "Unit-Distance Error-Checking Codes", IRE Trans. Electronic Computers, Vol. 7, pp 179-180, 1958.
  4. Kochut, K.J., "Snake-in-the-box codes for dimension 7", J Comb Math Comb Comput, Vol. 20, pp 175-185, 1996.
  5. Paterson, K.G. and Tuliani, J., "Some New Circuit Codes", IEEE Transactions on Information Theory, Vol. 44(3), pp 1305-1309, 1998.
  6. 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.
  7. 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.
  8. 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.
  9. Wynn, E., “Personal Communications”, (11/2009, dim 9 186), 8/2010, 1/13/2012. See also "Constructing Circuit Codes by Permuting Initial Sequences".
  10. 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.
  11. 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.
  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. Meyerson, S., Whiteside, W., Drapela, T., and Potter, W.D., latest experimental results: 7/2014.
  14. 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.
  15. Abbott, H., and Katchalski, M., “On The Construction of Snake In The Box Codes,” Utilitas Mathematica, 40, 97-116, 1991.

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