Graphs, maneuvers and turnpikes

The paper addresses the problem of moving a collection of objects from one subset of Z^m to another at minimum cost. It shows that under fairly natural rules for movement assumptions, if the origin and destination are far enough apart, then a near optimal solution with special structure exists: The present trajectory from the origin to the destination accrues almost all of its cost repeating at most m different patterns of movement. Directions for related research are identified.