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The Online Set Cover Problem Baruch Awerbuch

Summary: The Online Set Cover Problem
Noga Alon
Baruch Awerbuch
Yossi Azar
Niv Buchbinder
Joseph (Seffi) Naor
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 one-by-one. 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


Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University


Collections: Mathematics