**This is an old revision of the document!**

There have been publications on the snake-in-the-box problem for over 50 years now. This page provides you with almost all the major references available, including the first paper ever, on this problem.

- Abbott, H.L., and Katchalski, M., "On the Snake-in-the-Box Problem",
*J. Combin. Theory*, Vol. 45, pp 13-24, 1988.

- Abbott, H.L., and M. Katchalski, "Snakes and Pseudo-Snakes in Powers of Complete Graphs",
*Discrete Mathematics*, Vol. 68, pp 1-8, 1988.

- Abbott, H.L., and Katchalski, M., "Further Results on Snakes in Powers of Complete Graphs",
*Discrete Mathematics*, Vol. 91, pp 111-120, 1991.

- Abbott, H.L., and Katchalski, M., "On the Construction of Snake in the Box Codes",
*Utilitas Mathematica*, Vol. 40, pp 97-116, 1991.

- Abbott, H.L., and Katchalski, M., "Estimates for Snakes and Pseudo-Snakes" in k
_{n}^{d},*Utilitas Mathematica*, Vol. 43, pp 97-100, 1993.

- 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.

- Axenovich, M., and Martin, R., "A note on short cycles in a hypercube",
*Discrete Math*. Vol. 306, pp 2212-2218, 2006.

- Bishop, J., "Investigating the Snake-in-the-box problem with Neuroevolution", Department of Comp. Sci., University of Texas, Austin.

- Black W. L., "Electronic combination locks",
*Quart. Progress Report of the Research Laboratory of Electronics*, No. 73, Massachusetts Institute of Technology, Cambridge, Massachusetts, pp 232-233, April, 1964.

- Blass, U., Honkala, I., Karpovsky, M., and Litsyn, S., "Short dominating paths and cycles in the binary hypercube",
*Ann. Combin*, Vol. 5, pp 51–59, 2001.

- Carlson, B.P., "Rule Coding for Genetic Algorithms: An Alternative Solution to the Traveling Salesman Problem", in the
*Proceedings of the Inter. Conf. on Artificial Intelligence*, Las Vegas, NV, pp 878-883, June, 2002.

- 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.

- Casella, D.A., and Potter, W.D., "New Lower Bounds for the Coil-In-The-Box Problem: Using Evolutionary Techniques to Hunt for Coils", in the Proceedings of the
*International Conference on Computational Intelligence, Man-Machine Systems, and Cybernetics*, CIMMACS’05, CD Proceedings Paper No. 501-111, Miami, Florida, November 17-19, 2005.

- 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.

- Casella, D.A., and Potter, W.D., "New Lower Bounds for the Snake-In-The-Box Problem: Using Evolutionary Techniques to Hunt for Snakes", in
*Proceedings of the 18th International FLAIRS Conference*, pp 264-269, Clearwater Beach, Florida, May, 2005.

- Chebiryak, Y., Kroening, D, "An efficient SAT encoding of circuit snakes", in
*Proceedings of IEEE International Symposium on Information Theory and its Applications*, Auckland, New Zealand, pp 1235–1238, December 7-10, 2008.

- Chebiryak, Y., Wahl, T., Kroening, D., and Haller, L., "Finding Lean Induced Cycles in Binary Hypercubes", in
*Proceedings of SAT Conference*, Lecture Notes in Computer Science no. 5584, Springer Verlag, pp 18-31, June, 2009.

- Chien, R.T., Freiman, C.V., and Tang, D.T., "Error connection and circuits on the n-cube", in the
*Proceedings of the 2nd Allerton Conference on Circuit and System Theory*, Univ of Illinois, Monitcello, Illinois, pp 899-912, September 28-30, 1964.

- Danzer, L., and Klee, V., "Lengths of Snakes in Boxes",
*J. Combinatorial Theory*, Vol. 2, pp 258-265, 1967.

- Davies, D.W., "Longest -Separated- Paths and Loops in an N Cube",
*IEEE Trans. Electronic Computers*, Vol. 14, p. 261, 1965.

- Deimer, K., "Some new bounds for the maximum length of circuit codes",
*IEEE Transactions on Information Theory*, Vol. 30, pp 754-756, 1984.

- Deimer, K., "A New Upper Bound for the Length of Snakes",
*Combinatorica*, Vol. 5(2), pp 109-120, 1985.

- Diaz-Gomez, P., and Hougen, D., "Genetic algorithms for hunting snakes in hypercubes: fitness function analysis and open questions", in
*Seventh ACIS Intern Conf on Softw Eng, Artif Intell, Netw, and Parallel/Distrib Comput (SNPD’06)*. IEEE, Computer Society, Los Alamitos CA, pp 389-394, 2006.

- Diaz-Gomez, P., and Hougen, D., "The snake in the box problem: Mathematical Conjecture and a Genetic Algorithm Approach", In
*Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation*(Seattle, Washington, USA, July 08 - 12, 2006). GECCO '06. ACM, New York, NY, pp 1409-1410.

- Dixon, E., and Goodman, S., "On the Number of Hamilton Circuits in the n-Cube", in the
*Proceedings of the American Mathematical Society*, Vol. 50, pp 500-504, July, 1975.

- Dontas, K, and De Jong, K., "Discovery of maximal distance codes using Genetic Algorithm", in the
*Proceedings of the 2nd International IEEE Conference on Tools for Artificial Intelligence*, pp 805- 811, 1990.

- Douglas, R.J., "Some results on the Maximum Length of Circuits of Spread k in the d-Cube",
*J. Combin. Theory*, Vol. 6, pp 323-339, 1969.

- Douglas, R.J., "Upper Bounds on the lengths of circuits of even spread in the d-cube",
*J. Combin. Theory*, Vol. 7, pp 206-214, 1969.

- Emelyanov, P.G., and Lukito, A., "On the maximal length of a snake in hypercubes of small dimension", in
*Discrete Mathematics*, Vol. 218, pp 51-59, 2000.

- Etzion, T., and Paterson, K.G., "Near optimal single-track Gray codes", in
*IEEE Transactions on Information Theory*, Vol. 42, pp 779-789, 1996.

- Evdokimov, A.A., “"Maximal length of a chain in a unit n-dimensional cube,
*Mat. Zametki*, Vol. 6, pp 306-319, 1969.

- Even, S., "Snake in the Box Codes", correspondence in
*IRE Transactions on Electronic Computers*, Vol. EC-12, p. 18, 1963.

- Harary, F., Hayes, J.P., and Wu, H.J., "A survey of the theory of hypercube graphs",
*Comput. Math. Applic.*, Vol. 15, pp 277-289, 1988.

- Haryanto, L., and van Zanten, A.J., "Snake-in-the-box codes and Euclidean Geometries", in
*Proceedings of the Ninth International Workshop ACCT*, Kranevo, Bulgaria, pp 208–213, June, 2004.

- Haryanto, L., "Constructing Snake-In-The-Box Codes and Families of such Codes Covering the Hypercube", Ph.D. Dissertation (A.J. van Zanten, advisor), Delft University of Technology, Delft, the Netherlands, 2007.

- Hiltgen, A.P., and Paterson K.G., "Single Track Circuit Codes,
*IEEE Transactions on Information Theory*, Vol. 47, pp 2587-2595, 2000.

- Juric, M., Potter, W.D., and Plaksin, M., "Using PVM for Hunting Snake In The Box Codes",
*Proceedings of the 1994 Transputer Research and Applications Conference (NATUG-7)*, pp 97-102, Athens, GA, October, 1994.

- Kautz, W.H., "Unit-Distance Error-Checking Codes",
*IRE Trans. Electronic Computers*, Vol. 7, pp 179-180, 1958.

- Kim, S., and Neuhoff, D.L., “"Snake-in-the-box codes as robust quantizer index assignments”, in
*Proceedings of IEEE International Symposium on Information Theory*, p 402, June 25-30, 2000.

- Klee, V., "A method for constructing circuit codes",
*J. Assoc. Comput. Mach.*, Vol. 14, pp 520-538, 1967.

- Klee, V., "What is the maximum length of a d-dimensional snake?",
*Amer. Math. Monthly*, Vol. 77, pp 63-65, 1970.

- Klee, V., "The Use of Circuit Codes in Analog-to-Digital Conversion",
*Graph Theory and its Applications*(B.Harris, ed.), Academic Press, New York, pp 121-131, 1970.

- Kochut, K.J., "Snake-in-the-box codes for dimension 7",
*J Comb Math Comb Comput*, Vol. 20, pp 175-185, 1996.

- Krafka, K.J., "The Snake-in-the-Box Problem",
*ACMSE '10*, Oxford, MS, USA, April 15-17, 2010.

- Lukito, A., and van Zanten, A.J., "A new non-asymptotic upper bound for snake-in-the-box codes", in
*Journal of Combinatorial Mathematics and Combinatorial Computing*, Vol. 39, pp 147-156, 2001.

- Lukito, A., and van Zanten, A.J., "Vertex Partitions of Hypercubes into Symmetric Snakes",
*Electronic Notes in Discrete Mathematics*, Vol. 11, pp 459-467, 2002.

- Palani, A., and Potter, W.D., “Hypercube Snake-In-The-Box Exploration Using Level Representation”, in the
*Proceedings of the 18th IMACS World Congress on Computational and Applied Mathematics & Applications in Science and Engineering*, Athens, Georgia, August, 2009 (to appear).

- 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.

- Preparata, F., and Nievergelt, J., "Difference-preserving codes",
*IEEE Transactions on Information Theory*, Vol. 20, pp 643-649, 1974.

- Rajan D.S., and Shende A.M., "Maximal and Reversible Snakes in the Hypercube", in
*Proceedings of the Annual Australian Conference on Combinatorial Mathematics and Combinatorial Computing*, 1999.

- Ramanujacharyulu, C., and Menon, V.V., "A note on the snake-in-the-box problem",
*Publ. Inst. Statist. Univ. Paris 13*, pp 131–135, 1964.

- Rickabaugh, B.P., and Shende, A.M., "Using PVM to Hunt Maximal Snakes in Hypercubes",
*Journal of Computing in Small Colleges*Volume 14 (2), pp 76-84, 1998.

- Shende, A.M., "Searching for Patterns of Snakes in Hypercubes",
*Journal of Computing Sciences in Colleges*, Volume 16 (2), pp 168-176, 2001.

- Singleton, R.C., "Generalized Snake-in-the-Box Codes", IEEE Trans.
*Electronic Computers*, Vol. 15, pp 596-602, 1966.

- Smith, B.A., "A Survey of Approaches to Snake-in-the-Box Construction",
*Technical Report*, University of Georgia, 2006.

- Snevily, H.S., "The Snake-in-the-Box Problem: A New Upper Bound",
*Discrete Math*, vol. 133, pp 307–314, 1994.

- Solov’jeva, F.I., "An Upper Bound for the Length of a Cycle in an n-Dimensional Unit Cube",
*Discret. Analiz.*, Vol. 45, pp 71-76, 1987. [English Translation]

- 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.

- Vasil’ev, Ju. I., "On the length of a cycle in an n-dimensional unit cube",
*Soviet Math. Dokl.*, Vol. 4, pp 160-163, 1963.

- Wang, L., and Potter, W.D., “SIB Code Search Based on Temporal Difference Learning”, in the
*Proceedings of the 18th IMACS World Congress on Computational and Applied Mathematics & Applications in Science and Engineering*, Athens, Georgia, August, 2009 (to appear).

- Wojciechowski, J., "A new lower bound for Snake-in-the-Box codes",
*Combinatorica*, Vol. 9, pp 91-99, 1989.

- Wojciechowski, J., "Covering the Hypercube with a Bounded Number of Disjoint Snakes",
*Combinatorica*, Vol. 14, pp 1-6, 1994.

- Wojciechowski, J., "ong Snakes in Powers of the Complete Graph With an Odd Number of Vertices",
*Journal of London Mathematical Society*, Vol. 50 (3), pp 465-476, 1994.

- Wojciechowski, J., "On the Length of Snakes in Powers of Complete Graphs",
*J. London Math. Soc.*, Vol. 71 (1), pp 22-32, 2005.

- Wong, C., and Sawada, J.,"Exhaustive Search for Maximal Length Coil-In-The-Box Codes",
*University of Guelph Technical Report*(TR-UG-CIS-2008-001), Guelph, Ontario, Canada, June, 2008.

- Wyner, A.D., "Note on Circuits and Chains of Spread k in the n-Cube",
*IEEE Transactions on Computers*, Vol. 20 (4), p. 474, April, 1971.

- Yehezkeally, Y., and Schwartz, M.,"Snake-in-the-Box Codes for Rank Modulation", Submitted: http://arxiv.org/abs/1107.3372v1

- van Zanten, A.J., and Haryanto, L., "Sets of disjoint snakes based on a Reed-Muller code and covering the hypercube", in
*Designs, Codes, and Cryptography*, Vol. 48, pp 207-229, 2008.

- van Zanten, A.J., and Lukito, A., "Construction of Certain Cyclic Distance-Preserving Codes Having Linear-Algebraic Characteristics",
*Designs, Codes, and Cryptography*, Vol. 16 (2), pp 185-199, 1999.

- Zemor, G., "An Upper Bound on the Size of the Snake-In-The-Box", in
*Combinatorica*, Vol. 17 (2), pp 287-298, 1997.

- Zinovik, I., Chebiryak, Y., and Kroening, D.,"Periodic Orbits and Equilibria in Glass Models for Gene Regulatory Networks",
*IEEE Transactions on Information Theory*, Vol. 56 (2), p. 805-820, February, 2010.

- Xianjuan Lu, “Hunting for Snakes Using Simulated Annealing”, 1994.

- Shilpa Hardas, "An Ant Colony Approach to the Snake-in-the-Box Problem", 2005.

- Chris Taylor, "A Comprehensive Framework for the Snake-in-the-Box Problem", 2007.

- Eric Drucker, "Exploring Applications of External Optimization", 2009.