Read with interest this breakthrough in the ‘traveling salesperson problem’. This famous computational problem has fascinated and obsessed mathematicians and computer scientists for decades.
Given a set of points, and the distances between them, what is the shortest route that a travelling salesman can take to visit all the points?
Finding an exact solution is possible, but takes a lot of computation. An approximate solution, guaranteed to be at most 50% longer than the shortest possible route, can be found much more easily. Is it possible to do better than this? E.g. can we efficiently find a route that is at most 49% longer than the best one? That has proved very hard to answer.
But this latest algorithm, devised by graduate student Nathan Klein and his advisers, managed to do this. It efficiently produces a route that is *slightly* less than 50% longer – by 0.2 billionth of a trillionth of a trillionth of a percent! But it is a major breakthrough, and will surely be improved on in time. In scientific and mathematical research, progress is gradual and cumulative. – LHL
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