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Informally, an algorithm is a set of explicit instructions used to solve a problem (e.g. Euclid's algorithm for computing the greatest common divisor of two integers). For more specific questions on algorithms, this tag may be used in conjunction with the approximation-algorithms, algorithmic-randomness and algorithmic-topology tags.
2
votes
Enumerating a type of two-color cycle
Google reveals many such algorithms. I'm not sure which one suits your needs. No efficient algorithms exist, as along the way you would find Hamiltonian paths, which is an NP-complete problem. …
2
votes
Building optimal rewriting rules.
The trie data structure seems to be precisely the structure you are looking for. It is more efficient in terms of both space and time than providing a table of rewrite rules. There are quite a few ref …
4
votes
Solving a system of linear inequalities -- what is the dimension of the solution set?
These notes by Ted Ralphs, Lehigh University, give you an answer to question 2, computing the dimension.