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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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Efficient algorithm for a distance on strings

Let $(M,d)$ be a metric space. Consider two sequences $a = (a_i)_{i=1}^n$, $b = (b_i)_{i=1}^m$, $n, m \in \mathbb{N}$ with elements in $M$. For two sequences $[n],[m]$, call $$\Gamma([n], [m]) = \big\ …