Diversity of solutions: An exploration through the lens of fixed-parameter tractability theory

•Parameterized analysis of a general notion of diversity of solutions that suits a large class of combinatorial problems.•Introduction of the notion of dynamic programming core.•Efficient dynamic cores for computing one solution yield efficient dynamic cores for computing a diverse set of solutions....

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Veröffentlicht in:Artificial intelligence Jg. 303; S. 103644
Hauptverfasser: Baste, Julien, Fellows, Michael R., Jaffke, Lars, Masařík, Tomáš, de Oliveira Oliveira, Mateus, Philip, Geevarghese, Rosamond, Frances A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.02.2022
Elsevier Science Ltd
Elsevier
Schlagworte:
Algorithms
Combinatorial analysis
Combinatorial optimization
Computational Complexity
Computer Science
Data Structures and Algorithms
Discrete Mathematics
Diversity
Dynamic programming
Parameters
Polynomials
Tree decomposition
Tree decomposition
Dynamic programming
Combinatorial optimization
Diversity
ISSN:0004-3702, 1872-7921
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Zusammenfassung:•Parameterized analysis of a general notion of diversity of solutions that suits a large class of combinatorial problems.•Introduction of the notion of dynamic programming core.•Efficient dynamic cores for computing one solution yield efficient dynamic cores for computing a diverse set of solutions.•The notion of diversity of solutions is also compatible with certain notions of kernel. 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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ISSN:0004-3702
1872-7921
DOI:10.1016/j.artint.2021.103644