Online computation and competitive analysis
Online computation and competitive analysis
On-line analysis of the TCP acknowledgment delay problem
Journal of the ACM (JACM)
On the remote server problem or more about TCP acknowledgments
Theoretical Computer Science
On the on-line rent-or-buy problem in probabilistic environments
Journal of Global Optimization
Competitive analysis of two special online device replacement problems
Journal of Computer Science and Technology
Price fluctuations: to buy or to rent
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
On the best possible competitive ratio for multislope ski rental
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Hi-index | 5.23 |
Suppose that some job must be done for a period of unspecified duration. The market offers a selection of devices that can do this job, each characterized by purchase and running costs. Which of them should we buy at what times, in order to minimize the total costs? As usual in competitive analysis, the cost of an on-line solution is compared to the optimum costs paid by a clearvoyant buyer. This problem which generalizes the basic rent-to-buy problem has been introduced by Azar et al. In the so-called convex case where lower running costs always imply higher prices, a strategy with competitive ratio 4+2√2 ≈ 6.83 has been proposed. Here we consider two natural subcases of the convex case in a continuous-time model where new devices can be bought at any time. For the static case where all devices are available at the beginning, we give a simple 4-competitive deterministic algorithm, and we show that 3.618 is a lower bound. (This is also the first non-trivial lower bound for the convex case, both for discrete and continuous time.) Furthermore, we give a 2.88-competitive randomized algorithm. In the case that all devices have equal prices but are not all available at the beginning, we show that a very simple algorithm is 2-competitive, and we derive a 1.618 lower bound.