The.Algorithm.Design.Manual.Springer-Verlag.1998

War Story: Nothing but Nets
``Well, it takes some time for the robot to come up to speed. We should probably also factor in
acceleration and deceleration of the arms.''
``Darn right. The more accurately you can model the time your arm takes to move between two points,
the better our solution will be. But now we have a very clean formulation. Let's code it up and let's see
how well it works!''
They were somewhat skeptical whether this approach would do any good, but they agreed to think about
it. A few weeks later they called me back and reported that the new algorithm reduced testing time by
about 30% over their previous approach, at a cost of a little more computational preprocessing. However,
since their testing machine costs $200,000 a pop and a PC costs $2,000, this is an excellent tradeoff. It is
particularly advantageous since the preprocessing need only be done once when testing multiple
instances of the same board.
The key idea leading to the successful solution was knowing how to model the job in terms of classical
algorithmic graph problems. I smelled TSP the instant they started talking about minimizing robot
motion. Once I realized that they were implicitly forming a star-shaped spanning tree to ensure
connectivity, it was natural to ask whether a minimum spanning tree would perform any better. This idea
led to a natural way to think about clustering, and thus partitioning each net into smaller nets. Finally, by
carefully constructing our distance metric to accurately model the costs of the robot itself, we get to
incorporate quite complicated properties (such as acceleration and differences between horizontal and
vertical speeds) without changing our fundamental graph model or algorithm design.
Next: War Story: Dialing for Up: Graph Algorithms Previous: All-Pairs Shortest Path
Algorithms
Mon Jun 2 23:33:50 EDT 1997
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