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So what's next after CLRS?
I've stumbled across this book and have learned a lot of stuff but I find many of the proofs really incomprehensible and I end up searching proofs elsewhere. Should I just push through or is there a better option?
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You can try using Cook
>after CLRS
algorithms spreads out very widely to the point where there are few books covering a single type. The closest is maybe Erik Demaine's advanced algorithms course on MIT OCW. But some topics are
>randomized/sublinear algorithms
>sketching algorithms
>geometric algorithms
>spectral methods and Laplacians
>analytic combinatorics (aka advanced analysis of algorithms)
>quantum algorithms
>distributed algorithms
>cache oblivious algorithms
>algebraic algorithms (i.e. those for computing group/ring/field properties efficiently)
>algorithms for topological data analysis (related to the above)
and so on.
Check out proof based (linear) algebra, graph theory, Theory of computation,... books to build a better intuition. Then revisit the book
Try reading Rudin's book on the topic
Two nice books:

Randomized Algorithms - Rajeev Motwani, Prabhakar Raghavan

Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis 2nd Edition
- Michael Mitzenmacher, Eli Upfal
OP clearly states that they want to learn combinatorial optimization but they are having difficulty with Korte and Vygen. The answer isn't to ask them to clarify what they want to learn.

You could use Cook, that's a good suggestion.
There's also the copy of the 1st course in Combinatorial Opt by Goemans at MIT which has a bibliography, PSets and notes: https://math.mit.edu/~goemans/18433S15/18433.html

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