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.
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Ito, H., Langerman, S., Yoshida, Y. (2012). Algorithms and Complexity of Generalized River Crossing Problems. In: Kranakis, E., Krizanc, D., Luccio, F. (eds) Fun with Algorithms. FUN 2012. Lecture Notes in Computer Science, vol 7288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30347-0_24
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DOI: https://doi.org/10.1007/978-3-642-30347-0_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30346-3
Online ISBN: 978-3-642-30347-0
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