A Note on the Complexity of a Simple Transportation Problem

Consider the problem of using a vehicle to transport k objects one at a time between s stations on a circular track. Let the cost of the transportation be the rotal distance traveled by the vehicle on the track. An 0 (k + M(s, q)) time algorithm is presented to find a minimum cost transportation, where M (m, n) is the time to solve a minimum spanning tree problem on a graph with m edges and n venices, and q ~ min{k, s} is the nwnber of strongly connected components in an associated balanced problem. Also, the minimum spanning tree problem on a graph with m edges and n vertices is reduced ro a transportation problem on a linear track with 0 (m) stations, 0 (m) objects and 0 (n) strongly connected components in 0 (m) time.