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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.

2 votes
1 answer
161 views

Optimization over permutation

The Problem This is the problem I am working on: Given a set $X = \{x_1, x_2, \cdots , x_n\}$ in a metric space, find an optimal ordering $\pi : X \rightarrow X$ that maximizes the following objective …
2 votes
1 answer
109 views

How to prove the local search algorithm can find the maximum weight independent set in a mat...

I am trying to prove a simple local search algorithm could solve exactly this problem: $\underset{S \in I(M), |S|=k}{max} c(S)$ where $M$ is a matroid, and $ I(M)$ is the set of all independent set, …