A New Structured Knight Tour Algorithm by Four Knights with Heuristic Preset Rules
Keywords:
Heuristic, Knight Tour, Preset Rules, Structural,Abstract
A Knight Tour problem is an ancient puzzle which remains as a focus of current researcher. The objective of a Knight Tour algorithm is to find out a solution with construct a closed moving path by a knight for visiting each square of a chessboard by only once. This paper proposes a new structural Knight Tour algorithm by four knights moving all together with heuristic preset rules. This new proposed method fulfills any board size of 4n+2 where n>1 with lower execution time and without the needs of any brute force method and backtracking method.References
L. Euler, “Solution d’une question curieuse que ne paroit soumise a aucune analyse,” in Mémoires de l’Academie Royale des Sciences et Belles Lettres, 1759, pp. 310–337.
I. Parberry, “An efficient algorithm for the Knight’s tour problem,” Discret. Appl. Math., vol. 73, no. 3, pp. 251–260, 1997.
S. S. Lin and C. L. Wei, “Optimal algorithms for constructing knight’s tours on arbitrary n×m chessboards,” Discret. Appl. Math., vol. 146, no. 3, pp. 219–232, 2005.
L. Paris, “Heuristic Strategies for the Knight Tour Problem,” in Proc. Int. Conf. Artif. Intell. IC-AI ’04, Vol. 2 Proc. Int. Conf. Mach. Learn. Model. Technol. Appl. MLMTA ’04, June 21-24, 2004, Las Vegas, Nevada, USA, pp. 4–8, 2004.
R. Borrell, “A brute force approach to solving the knight’s tour problem using Prolog,” in Proc. 2009 Int. Conf. Artif. Intell. ICAI 2009, vol. 2, 2009.
M. M. Ismail, A.F. Zainal Abidin, S. Widiyanto, M.H. Misran, M. Alice, N.A. Nordin, E.F. Shair, S.M. Mustaza, M.N. Shah Zainudin, “Solving Knight’s tour problem using firefly algorithm,” in the Proc. 3rd Int. Conf. Eng. ICT, no. April, pp. 5–8, 2012.
W. W. R. Ball, Mathematical Recreations and Essays, 12th ed. New York, USA: MacMillan, 1939.
H. E. Dudeney, Amusements in Mathematics, Thomson Nelson and Sons Ltd. London, 1917.
A. P. Domoryad, Mathematical Games and Pastimes. Oxford, 1964.
S. P. Hurd and D. A. Trautman, “The Knight’s Tour on the 15-puzzle,” Math. Mag., vol. 66, no. 3, p. 159, Jun. 1993.
K. Lim, “The Knight’s tour,” Parabola, no. 1, UNSW Australia, Sydney, 1981.
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