Randomized algorithms
Improved approximations of packing and covering problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
A tight analysis of the greedy algorithm for set cover
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Approximation algorithms
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
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
Tight approximability results for test set problems in bioinformatics
Journal of Computer and System Sciences
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
Hi-index | 5.23 |
In this paper, we consider the weighted online set k-multicover problem. In this problem, we have a universe V of elements, a family S of subsets of V with a positive real cost for every S@?S, and a ''coverage factor'' (positive integer) k. A subset {i"0,i"1,...}@?V of elements are presented online in an arbitrary order. When each element i"p is presented, we are also told the collection of all (at least k) sets S"i"""p@?S and their costs to which i"p belongs and we need to select additional sets from S"i"""p if necessary such that our collection of selected sets contains at leastk sets that contain the element i"p. The goal is to minimize the total cost of the selected sets. In this paper, we describe a new randomized algorithm for the online multicover problem based on a randomized version of the winnowing approach of [N. Littlestone, Learning quickly when irrelevant attributes abound: A new linear-threshold algorithm, Machine Learning 2 (1988) 285-318]. This algorithm generalizes and improves some earlier results in [N. Alon, B. Awerbuch, Y. Azar, N. Buchbinder, J. Naor, A general approach to online network optimization problems, in: Proceedings of the 15th ACM-SIAM Symposium on Discrete Algorithms, 2004, pp. 570-579; N. Alon, B. Awerbuch, Y. Azar, N. Buchbinder, J. Naor, The online set cover problem, in: Proceedings of the 35th Annual ACM Symposium on the Theory of Computing, 2003, pp. 100-105]. We also discuss lower bounds on competitive ratios for deterministic algorithms for general k based on the approaches in [N. Alon, B. Awerbuch, Y. Azar, N. Buchbinder, J. Naor, The online set cover problem, in: Proceedings of the 35th Annual ACM Symposium on the Theory of Computing, 2003, pp. 100-105].