Diversity of solutions: An exploration through the lens of fixed-parameter tractability theory
Baste, Julien; Fellows, Michael Ralph; Jaffke, Lars; Masařík, Tomáš; Oliveira, Mateus De Oliveira; Philip, Geevarghese; Rosamond, Frances
Journal article, Peer reviewed
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Date
2022Metadata
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- Department of Informatics [1002]
- Registrations from Cristin [11365]
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.