Diverse Collections in Matroids and Graphs
Fedor V. Fomin, Petr A. Golovach, Fahad Panolan, Geevarghese, Philip, Saket Saurabh

TL;DR
This paper studies the computational complexity of finding diverse solution sets in matroids and graphs, introducing new NP-hard problems and providing fixed-parameter algorithms for them.
Contribution
It defines new diverse solution problems in matroid and graph theory and develops fixed-parameter tractable algorithms for these problems.
Findings
Weighted Diverse Bases and Common Independent Sets are NP-hard.
FPT algorithms are developed for all three problems with parameters (k,d).
The work extends classical matroid and graph problems to diverse solution variants.
Abstract
We investigate the parameterized complexity of finding diverse sets of solutions to three fundamental combinatorial problems, two from the theory of matroids and the third from graph theory. The input to the Weighted Diverse Bases problem consists of a matroid , a weight function , and integers . The task is to decide if there is a collection of bases of such that the weight of the symmetric difference of any pair of these bases is at least . This is a diverse variant of the classical matroid base packing problem. The input to the Weighted Diverse Common Independent Sets problem consists of two matroids defined on the same ground set , a weight function , and integers . The task is to decide if there is a collection of common independent sets…
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Taxonomy
TopicsOptimization and Packing Problems · Advanced Graph Theory Research · VLSI and FPGA Design Techniques
