The Traveler's Problem

The Traveler’s Problem (TP) entails determining the maximum distance that can be traversed along a road, given the locations and room rates of inns along that road, and given the constraints of maximum distance per day and limited budget available for overnight stays at inns. An OP(n 3 5_ (log n) 3 1_ ) time algorithm is presented for the TP. An OP(n 3 5_ (log n) 3 4_ )-time algorithm for computing a minimum height B-tree for a dictionary of length n is given, by reducing the problem to OP(log n) instances of the TP.