The weighted majority algorithm
Information and Computation
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Game theory, on-line prediction and boosting
COLT '96 Proceedings of the ninth annual conference on Computational learning theory
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Static optimality and dynamic search-optimality in lists and trees
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
On-line Algorithms in Machine Learning
Developments from a June 1996 seminar on Online algorithms: the state of the art
A general approach to online network optimization problems
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Admission control to minimize rejections and online set cover with repetitions
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
ACM SIGACT News
Greedy algorithms for on-line set-covering and related problems
CATS '06 Proceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 51
A general approach to online network optimization problems
ACM Transactions on Algorithms (TALG)
Competitiveness via primal-dual
ACM SIGACT News
Online make-to-order joint replenishment model: primal dual competitive algorithms
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating the online set multicover problems via randomized winnowing
Theoretical Computer Science
Non-cooperative Cost Sharing Games Via Subsidies
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Online and stochastic survivable network design
Proceedings of the forty-first annual ACM symposium on Theory of computing
Online Primal-Dual Algorithms for Covering and Packing
Mathematics of Operations Research
The Design of Competitive Online Algorithms via a Primal: Dual Approach
Foundations and Trends® in Theoretical Computer Science
Admission control to minimize rejections and online set cover with repetitions
ACM Transactions on Algorithms (TALG)
Online primal-dual algorithms for maximizing ad-auctions revenue
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Online set packing and competitive scheduling of multi-part tasks
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
An improved competitive algorithm for reordering buffer management
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Thresholded covering algorithms for robust and max-min optimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Inferring social networks from outbreaks
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Proceedings of the fourth ACM international conference on Web search and data mining
Selective regular expression matching
ISC'10 Proceedings of the 13th international conference on Information security
Online Optimization with Uncertain Information
ACM Transactions on Algorithms (TALG)
The node-weighted steiner problem in graphs of restricted node weights
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Online primal-dual algorithms for covering and packing problems
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Approximating the online set multicover problems via randomized winnowing
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
The covert set-cover problem with application to network discovery
WALCOM'10 Proceedings of the 4th international conference on Algorithms and Computation
Approximating sparse covering integer programs online
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Dynamic covering for recommendation systems
Proceedings of the 21st ACM international conference on Information and knowledge management
Using maximum coverage to optimize recommendation systems in e-commerce
Proceedings of the 7th ACM conference on Recommender systems
Greedy algorithms for on-line set-covering and related problems
CATS '06 Proceedings of the Twelfth Computing: The Australasian Theory Symposium - Volume 51
Hi-index | 0.00 |
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 problem, described as a game between an algorithm and an adversary. 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 chosen by the algorithm. Let C denote the family of sets in S that the algorithm chooses. At the end of the game the adversary also produces (off-line) a family of sets COPT that covers X'. The performance of the algorithm is the ratio between the cost of C and the cost of COPT. The maximum ratio, taken over all input sequences, is the competitive ratio of the algorithm.We present an O(log m log n) competitive deterministic algorithm for the problem, and establish a nearly matching Ω(log n log m/log log m + log log n) lower bound for all interesting values of m and n. The techniques used are motivated by similar techniques developed in computational learning theory for online prediction (e.g., the WINNOW algorithm) together with a novel way of converting the fractional solution they supply into a deterministic online algorithm.