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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.

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maximal sets of vertices that avoids a clique

The bad news is that HITTING-SET is NP-Complete but the good news: it is Fixed-parameter tractable and there are good exact algorithms for it is very well-studied there are fast approximation algorithms … the fewest number of vertices from subsets that have that property) there are implementations of the problem of finding the hitting set: https://github.com/VeraLiconaResearchGroup/Minimal-Hitting-Set-Algorithms
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