Republican presidential hopeful Mitt Romney begins his three-day tour of Iowa today in anticipation of next week’s caucuses. What is the optimal path for him to travel in order to hit all 99 counties?

This is a version of something known as “the traveling salesman problem,” one of the great unsolved problems in mathematics. But three professors specializing in the field of operations research appear to have solved “the traveling politician problem,” at least when it comes to Iowa.

Above is a map developed by William Cook, a professor of industrial and systems engineering at Georgia Tech, and Alain Kornhauser and Robert Vanderbei, professors of operations research and financial engineering at Princeton.

“The white path traces the quickest possible tour through the state, hitting all 99 county seats in 55.5 hours and 2,739 miles,” Cook explained in a recent opinion piece in The New York Times. “The trip is circular, so you can start and stop at any of the 99 and travel the same total distance.”

To construct the optimal tour, the professors had to compute point-to-point trips  from county seat to county seat for each pair of counties, adding up to nearly 10,000 individual trips. They did this by using a software called CoPilot developed by Kornhauser.

The colors in the map above are based on Vanderbei’s Purple America map, which shows Democatic counties in blue and Republican counties in red.