 
Summary: The Online Set Cover Problem
Noga Alon
Baruch Awerbuch
Yossi Azar
Niv Buchbinder §
Joseph (Seffi) Naor ¶
ABSTRACT
Let X = {1, 2, . . . , n} be a ground set of n elements, and let
S be a family of subsets of X, S = m, with a positive cost
cS associated with each S S.
Consider the following online version of the set cover prob
lem, described as a game between an algorithm and an ad
versary. An adversary gives elements to the algorithm from
X onebyone. Once a new element is given, the algorithm
has to cover it by some set of S containing it. We assume
that the elements of X and the members of S are known
in advance to the algorithm, however, the set X X of
elements given by the adversary is not known in advance
to the algorithm. (In general, X may be a strict subset of
X.) The objective is to minimize the total cost of the sets
