@inproceedings{967f0ceafa67407493785c19714a34b3,
title = "Online disjoint set cover without prior knowledge",
abstract = "The disjoint set cover (DSC) problem is a fundamental combinatorial optimization problem concerned with partitioning the (hyper)edges of a hypergraph into (pairwise disjoint) clusters so that the number of clusters that cover all nodes is maximized. In its online version, the edges arrive one-by-one and should be assigned to clusters in an irrevocable fashion without knowing the future edges. This paper investigates the competitiveness of online DSC algorithms. Specifically, we develop the first (randomized) online DSC algorithm that guarantees a poly-logarithmic (O(log2 n)) competitive ratio without prior knowledge of the hypergraph{\textquoteright}s minimum degree. On the negative side, we prove that the competitive ratio of any randomized online DSC algorithm must be at least (formula presented.) (even if the online algorithm does know the minimum degree in advance), thus establishing the first lower bound on the competitive ratio of randomized online DSC algorithms.",
keywords = "Competitive analysis, Competitiveness with high probability, Disjoint set cover, Online algorithms",
author = "Yuval Emek and Adam Goldbraikh and Erez Kantor",
note = "Publisher Copyright: {\textcopyright} Yuval Emek, Adam Goldbraikh, and Erez Kantor.; 27th Annual European Symposium on Algorithms, ESA 2019 ; Conference date: 09-09-2019 Through 11-09-2019",
year = "2019",
month = sep,
doi = "https://doi.org/10.4230/LIPIcs.ESA.2019.44",
language = "الإنجليزيّة",
series = "Leibniz International Proceedings in Informatics, LIPIcs",
editor = "Bender, {Michael A.} and Ola Svensson and Grzegorz Herman",
booktitle = "27th Annual European Symposium on Algorithms, ESA 2019",
}