An upper bound on . (Karp and Steele, 1985) The strips method for constructing a tour through n random points in the unit square dissects

An upper bound on β. (Karp and Steele, 1985) The strips method for constructing a tour through n random points in the unit square dissects the square into 1 7 horizontal strips of width 7, and then follows a zigzag path, visiting the points in the first strip in left-to-right order, then the points in the second strip in right-to-left order, etc., finally returning to the initial point from the final point of the last strip. Prove that, when 7 is suitably chosen, the expected length of the tour produced by the strips method is at most 1.16

√

n.