Graphs, Maneuvers, and Turnpikes

We address the problem of moving a collection of objects from one subset of Zm to another at minimum cost. We show that underfairly natural rules for movement assumptions, if the origin and destination are far enough apart, then a near optimal solution with special structure exists: Our trajectory from the originto the destination accrues almost all of its cost repeatingat most m different patterns of movement. Directions for related research are identified