Abstract
An irredundant set of a hypergraph \(G = (V,\mathcal {H})\) 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 \(O(2^d \varDelta ^{d+1} n^2)\), where d is the degeneracy of the hypergraph and \(\varDelta \) the maximum node degree. As \(d\le \varDelta \), we immediately obtain an algorithm with delay \(O(2^\varDelta \varDelta ^{\varDelta +1} n^2)\) 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.