From 55b55d1fc1672c348330684320ec338063beceae Mon Sep 17 00:00:00 2001 From: Antti H S Laaksonen Date: Mon, 17 Apr 2017 11:39:41 +0300 Subject: [PATCH] Reference to polynomial algorithms for knight's tour [closes #35] --- chapter19.tex | 8 +++++--- list.tex | 5 +++++ 2 files changed, 10 insertions(+), 3 deletions(-) diff --git a/chapter19.tex b/chapter19.tex index 1949b3f..8e27242 100644 --- a/chapter19.tex +++ b/chapter19.tex @@ -640,9 +640,11 @@ a complete tour will be found quickly. \index{heuristic} \index{Warnsdorf's rule} -\key{Warnsdorf's rule}\footnote{This heuristic was proposed -in Warnsdorf's book \cite{war23} in 1823.} is a simple and effective heuristic -for finding a knight's tour. +\key{Warnsdorf's rule} is a simple and effective heuristic +for finding a knight's tour\footnote{This heuristic was proposed +in Warnsdorf's book \cite{war23} in 1823. There are +also polynomial algorithms for finding knight's tours +\cite{par97}, but they are more complicated.}. Using the rule, it is possible to efficiently construct a tour even on a large board. The idea is to always move the knight so that it ends up diff --git a/list.tex b/list.tex index 9bf6ff6..8ae33c1 100644 --- a/list.tex +++ b/list.tex @@ -261,6 +261,11 @@ pro \emph{Annals of Mathematics}, 3(1/4):35--39, 1901. Where to use and how not to use polynomial string hashing. \emph{Olympiads in Informatics}, 7(1):90--100, 2013. +\bibitem{par97} + I. Parberry. + An efficient algorithm for the Knight's tour problem. + \emph{Discrete Applied Mathematics}, 73(3):251--260, 1997. + % \bibitem{pic99} % G. Pick. % Geometrisches zur Zahlenlehre.