Showing papers by "Michael R. Fellows published in 2020"

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

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.

Collaborating with Hans: Some Remaining Wonderments.

Abstract: This paper celebrates some family adventures, three concrete open problems and several research directions that have developed over our long collaboration.