Morphing: Combining Structure and Randomness

We introduce a mechanism called "morphing" for introducing structure or randomness into a wide variety of problems. We illustrate the usefulness of morphing by performing sever;tl different experimental studies. These studies identify the impact of a "small-world" topology on the cost of coloring graphs, of asymmetry on the cost of finding the optimal TSP tour, and of the dimensionality of space on the cost of finding the optimal TSP tour. We predict that morphing will find many other uses.