Algorithms and Complexity of Generalized River Crossing Problems

  • Hiro Ito
  • Stefan Langerman
  • Yuichi Yoshida
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7288)


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.


Polynomial Time Vertex Cover Left Bank River Crossing Famous Problem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Hiro Ito
    • 1
  • Stefan Langerman
    • 2
  • Yuichi Yoshida
    • 1
    • 3
  1. 1.School of InformaticsKyoto UniversityKyotoJapan
  2. 2.Maître de recherches du F.R.S.-FNRS, Département d’informatiqueUniversité Libre de Bruxelles (ULB)Belgium
  3. 3.Preferred Infrastructure, Inc.Japan

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