Power of human-algorithm collaboration in solving combinatorial optimization problems
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Many combinatorial optimization problems are often considered intractable to solve exactly or by approximation. An example of such problem is maximum clique which – under standard assumptions in complexity theory – cannot be solved in sub-exponential time or be approximated within polynomial factor efficiently. We show that if a polynomial time algorithm can query informative Gaussian priors from an expert poly(n) times, then a class of combinatorial optimization problems can be solved efficiently in expectation up to a multiplicative factor ϵ where ϵ is arbitrary constant. While our proposed methods are merely theoretical, they cast new light on how to approach solving these problems that have been usually considered intractable.
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