FPT Algorithms for Diverse Collections of Hitting Sets
Julien Baste, Lars Jaffke, Tom\'a\v{s} Masa\v{r}\'ik, Geevarghese, Philip, G\"unter Rote

TL;DR
This paper develops fixed-parameter tractable algorithms for finding diverse collections of solutions to the $d$-Hitting Set and Feedback Vertex Set problems, using network flow techniques to maximize diversity based on Hamming distances.
Contribution
It introduces a novel FPT approach for generating diverse solution collections in parameterized problems, employing a problem-independent network flow formulation.
Findings
Both problems are FPT in parameters k + r for the diversity measures.
A network flow formulation efficiently computes maximally diverse solution collections.
The approach addresses information loss in problem abstraction processes.
Abstract
In this work, we study the -Hitting Set and Feedback Vertex Set problems through the paradigm of finding diverse collections of solutions of size at most each, which has recently been introduced to the field of parameterized complexity [Baste et al., 2019]. This paradigm is aimed at addressing the loss of important side information which typically occurs during the abstraction process which models real-world problems as computational problems. We use two measures for the diversity of such a collection: the sum of all pairwise Hamming distances, and the minimum pairwise Hamming distance. We show that both problems are FPT in for both diversity measures. A key ingredient in our algorithms is a (problem independent) network flow formulation that, given a set of `base' solutions, computes a maximally diverse collection of solutions. We believe that this could be of…
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