Power of human-algorithm collaboration in solving combinatorial optimization problems

• URL: http://arxiv.org/abs/2107.11784v1
• Date: Sun, 25 Jul 2021 11:21:59 GMT
• Title: Power of human-algorithm collaboration in solving combinatorial optimization problems
• Authors: Tapani Toivonen
• Abstract summary: We show that a class of optimization problems can be solved efficiently in expectation up to a multiplicative factor $epsilon$ where $epsilon$ 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\epsilon$ where $\epsilon$ 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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