Algorithms and complexity of generalized river crossing problems

Authors:
Hiro Ito;Stefan Langerman;Yuichi Yoshida
Affiliations:
School of Informatics, Kyoto University, Kyoto, Japan;Maître de recherches du F.R.S.-FNRS, Département d'informatique, Université Libre de Bruxelles (ULB), Belgium;School of Informatics, Kyoto University, Kyoto, Japan,Preferred Infrastructure, Inc., Japan
Venue:
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
Year:
2012

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Abstract

Three men, each with a sister, must cross a river using a boat which can carry only two people, so that a woman whose brother is not present is never left in the company of another man. This is a very famous problem appeared in Latin book "Problems to Sharpen the Young," one of the earliest collections on recreational mathematics. This paper considers a generalization of such "River-Crossing Problems." It shows that the problem is NP-hard if the boat size is three, and a large class of sub-problems can be solved in polynomial time if the boat size is two. It's also conjectured that determining whether a river crossing problem has a solution without bounding the number of transportations, can be solved in polynomial time even when the size of the boat is large.