On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
Developments from a June 1996 seminar on Online algorithms: the state of the art
A general approach for incremental approximation and hierarchical clustering
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Incremental Medians via Online Bidding
Algorithmica
| Hi-index | 0.89 |
In the online bidding problem, a bidder is trying to guess a positive number T, by placing bids until the value of the bid is at least T. The bidder is charged with the sum of the bids. In the bounded online bidding problem, a parameter k is given, and the bidder is charged only with the largest k bids. It is known that the online bidding problem admits a 4-competitive deterministic algorithm, and an e-competitive randomized algorithm, and these results are best possible. The deterministic best possible competitive ratio for the online bounded bidding problem is also known, for any value of k. We study the randomized bounded online bidding problem, and show that for any k2, randomization is helpful, that is, it allows to design an algorithm of a smaller competitive ratio compared to the best deterministic algorithm. In contrast, for k=2, we show a lower bound of 2 on the competitive ratio of any randomized algorithms, matching the upper bound achieved by a trivial deterministic algorithm, which tests all possible bids sequentially.