Curves of Width One and the River Shore Problem
Timothy M. Chan, Alexander Golynski, Alejandro López-Ortíz, Claude-Guy Quimper · 2003
We consider the problem of nding the shortest curve in the plane that has unit width. This problem was rst posed as the \\river shore" puzzle by Ogilvy (1972) and is related to the area of on-line searching. Adhikari and Pitman (1989) proved that the optimal solution has length 2:2782 : : : We present a simpler proof, which exploits the fact that the width of a polygon does not decrease under a certain convexi cation operation.