Here are a few areas that you could explore for implementing and publishing a new algorithm in Rust:

- Graph algorithms: This includes algorithms for graph theory such as shortest path, minimum spanning tree, and graph traversal algorithms like depth-first search and breadth-first search.

- Sorting algorithms: You could implement and publish various sorting algorithms like bubble sort, insertion sort, quick sort, and so on.

- Machine learning algorithms: You could implement algorithms such as linear regression, k-nearest neighbors, and decision trees, and make them available as a Crate.

- Data structures: You could implement various data structures such as linked lists, trees, heaps, and hash maps, and make them available as a Crate.

- Cryptographic algorithms: You could implement and publish cryptographic algorithms like AES, RSA, and SHA-256.
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