11 research outputs found
Minimal dominating sets enumeration with FPT-delay parameterized by the degeneracy and maximum degree
At STOC 2002, Eiter, Gottlob, and Makino presented a technique called ordered
generation that yields an -delay algorithm listing all minimal
transversals of an -vertex hypergraph of degeneracy . Recently at IWOCA
2019, Conte, Kant\'e, Marino, and Uno asked whether this XP-delay algorithm
parameterized by could be made FPT-delay parameterized by and the
maximum degree , i.e., an algorithm with delay for some computable function . Moreover, as a first step toward
answering that question, they note that the same delay is open for the
intimately related problem of listing all minimal dominating sets in graphs. In
this paper, we answer the latter question in the affirmative.Comment: 18 pages, 2 figure
Maximal irredundant set enumeration in bounded-degeneracy and bounded-degree hypergraphs
An irredundant set of a hypergraph G = (V,H) is a subset S of its nodes such that removing any node from S decreases the number of hyperedges it intersects. The concept is deeply related to that of dominating sets, as the minimal dominating sets of a graph correspond exactly to the dominating sets which are also maximal irredundant sets. In this paper we propose an FPT-delay algorithm for listing maximal irredundant sets, whose delay is O(2dΔd+1n2), where d is the degeneracy of the hypergraph and Δ the maximum node degree. As d ≤ Δ,, we immediately obtain an algorithm with delay O(2ΔΔΔ+1n2) that is FPT for bounded-degree hypergraphs. This result opens a gap between known bounds for this problem and those for listing minimal dominating sets in these classes of hypergraphs, as the known running times used to be the same, hinting at the idea that the latter may indeed be harder
LIPIcs, Volume 274, ESA 2023, Complete Volume
LIPIcs, Volume 274, ESA 2023, Complete Volum