TY - GEN
T1 - Online disjoint set cover without prior knowledge
AU - Emek, Yuval
AU - Goldbraikh, Adam
AU - Kantor, Erez
N1 - Publisher Copyright:
© Yuval Emek, Adam Goldbraikh, and Erez Kantor.
PY - 2019/9
Y1 - 2019/9
N2 - 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’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.
AB - 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’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.
KW - Competitive analysis
KW - Competitiveness with high probability
KW - Disjoint set cover
KW - Online algorithms
UR - http://www.scopus.com/inward/record.url?scp=85074834219&partnerID=8YFLogxK
U2 - 10.4230/LIPIcs.ESA.2019.44
DO - 10.4230/LIPIcs.ESA.2019.44
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AN - SCOPUS:85074834219
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 27th Annual European Symposium on Algorithms, ESA 2019
A2 - Bender, Michael A.
A2 - Svensson, Ola
A2 - Herman, Grzegorz
T2 - 27th Annual European Symposium on Algorithms, ESA 2019
Y2 - 9 September 2019 through 11 September 2019
ER -