کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
10328700 684868 2005 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Optimal algorithms for constructing knight's tours on arbitrary n×m chessboards
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نظریه محاسباتی و ریاضیات
پیش نمایش صفحه اول مقاله
Optimal algorithms for constructing knight's tours on arbitrary n×m chessboards
چکیده انگلیسی
The knight's tour problem is an ancient puzzle whose goal is to find out how to construct a series of legal moves made by a knight so that it visits every square of a chessboard exactly once. In previous works, researchers have partially solved this problem by offering algorithms for subsets of chessboards. For example, among prior studies, Parberry proposed a divided-and-conquer algorithm that can build a closed knight's tour on an n×n, an n×(n+1) or an n×(n+2) chessboard in O(n2) (i.e., linear in area) time on a sequential processor. In this paper we completely solve this problem by presenting new methods that can construct a closed knight's tour or an open knight's tour on an arbitrary n×m chessboard if such a solution exists. Our algorithms also run in linear time (O(nm)) on a sequential processor.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Applied Mathematics - Volume 146, Issue 3, 15 March 2005, Pages 219-232
نویسندگان
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