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Combinatorial optimization typically deals with optimizing over a finite set of objects that have some combinatorial structure (e.g. trees, matchings, matroids). Approximation algorithms, polyhedral methods, and integer programming are all on topic.
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Upper bounds on the worst-case traveling salesman tours in the unit square
For n=6 the optimal solution is the four corners and two points on the diagonal, roughly at (0.4, 0.4) and (0.6, 0.6). The optimal length is 4.571326...
There are newer results than the 1955 paper, se …