The Closed Knight Tour Problem in Higher Dimensions
نویسندگان
چکیده
منابع مشابه
The Closed Knight Tour Problem in Higher Dimensions
The problem of existence of closed knight tours for rectangular chessboards was solved by Schwenk in 1991. Last year, in 2011, DeMaio and Mathew provide an extension of this result for 3-dimensional rectangular boards. In this article, we give the solution for n-dimensional rectangular boards, for n > 4.
متن کاملHeuristic Strategies for the Knight Tour Problem
This paper presents three heuristic functions that aim to reduce the search cost for the knight tour problem. The first heuristic, h1a, is an interesting case of study that illustrates heuristic analysis, although it fails to obtain solutions. Heuristic h2 is an enhancement of the Warnsdorff method, discussed as heuristic h1b. All heuristics are used in conjunction with a greedy algorithm to de...
متن کاملThe n-queens problem in higher dimensions
The 8-queens problem is a well-known chessboard problem, whose constraints are to place eight queens on a normal chessboard in such a way that no two attack each other, under the rule that a chess queen can attack other pieces in the same column, row, or diagonal. This problem can be generalized to place n queens on an n by n chessboard, otherwise known as the n-queens problem. The mathematicia...
متن کاملComplex Analysis: A Brief Tour into Higher Dimensions
1. INTRODUCTION. Why is it that most graduate students of mathematics (and many undergraduates as well) are exposed to complex analysis in one variable, yet only a small minority of students or, for that matter, professional mathematicians ever learn even the most basic corresponding theory in several variables? Think about it another way: Could anyone seriously argue that it might be sufficien...
متن کاملEinstein Straus Problem in Higher Dimensions
Years ago Einstein and Straus (ES) showed that it is possible to match a static Schwarzschild region to an external expanding Friedmann universe. This model is extended in this work to a spacetime of arbitrary dimensions. Frequency shift of radiation coming from the boundary of the two spacetimes is calculated. Depending on the relative magnitude of gravitational and doppler effects our model g...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2012
ISSN: 1077-8926
DOI: 10.37236/2272