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arXiv · 1903.07410

Diversity of Solutions: An Exploration Through the Lens of Fixed-Parameter Tractability Theory

Julien Baste·Michael R. Fellows·Lars Jaffke·Tomáš Masařík·Mateus de Oliveira Oliveira·Geevarghese Philip·Frances A. Rosamond
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Abstract

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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Julien Baste, Michael R. Fellows, Lars Jaffke, Tomáš Masařík, Mateus de Oliveira Oliveira, Geevarghese Philip, Frances A. Rosamond. 2019-03-18. Diversity of Solutions: An Exploration Through the Lens of Fixed-Parameter Tractability Theory. https://doi.org/10.1016/j.artint.2021.103644%2010.24963%2Fijcai.2020%2F156

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