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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
Optimal Graph Splitting
Both of these problems share many similarities with the partition problem for which there exists efficient greedy algorithms, dynamic programming approaches, and exact methods (see link).
1
vote
Distribution of a knapsack problem
The optimal value of $p(A)$ can easily be found by ordering the items by nonincreasing profits, and packing the first $M$ items into the knapsack. The average value of a packing is $(\sum_{i \in N}p_{ …