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تسجيل مستخدم جديدDiversity of Solutions: An Exploration Through the Lens of Fixed-Parameter Tractability Theory
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نشر من قبل
Tom\\'a\\v{s} Masa\\v{r}\\'ik
تاريخ النشر
2019
مجال البحث
الهندسة المعلوماتية
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English
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When modeling an application of practical relevance as an instance of a combinatorial problem X, we are often interested not merely in finding one optimal solution for that instance, but in finding a sufficiently diverse collection of good solutions. In this work we initiate a systematic study of diversity from the point of view of fixed-parameter tractability theory. First, we consider an intuitive notion of diversity of a collection of solutions which suits a large variety of combinatorial problems of practical interest. We then present an algorithmic framework which --automatically-- converts a tree-decomposition-based dynamic programming algorithm for a given combinatorial problem X into a dynamic programming algorithm for the diverse version of X. Surprisingly, our algorithm has a polynomial dependence on the diversity parameter.
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