Showing papers by "Ran El-Yaniv published in 1999"

Competitive Optimal On-Line Leasing

Abstract: Consider an on-line player who needs some equipment (e.g., a computer) for an initially unknown number of periods. At the start of each period it is determined whether the player will need the equipment during the current period and the player has two options: to pay a leasing fee c and rent the equipment for the period, or to buy it for a larger amount P. The total cost incurred by the player is the sum of all leasing fees and perhaps one purchase. The above problem, called the leasing problem (in computer science folklore it is known as the ski-rental problem), has received considerable attention in the economic literature. Using the competitive ratio as a performance measure this paper is concerned with determining the optimal competitive on-line policy for the leasing problem. For the simplest version of the leasing problem (as described above) it is known and readily derived that the optimal deterministic competitive performance is achieved by leasing for the first ki 1 times and then buying, where kD P=c. This strategy pays at most 2i 1=k times the optimal off-line cost. When considering alternative financial transactions one must consider their net present value. Thus, ac- counting for the interest rate is an essential feature of any reasonable financial model. In this paper we deter- mine both deterministic and randomized optimal on-line leasing strategies while accounting for the interest rate factor. It is shown here, for the leasing problem, that the interest rate factor reduces the uncertainty involved. We find that the optimal deterministic competitive ratio is 1C.1C i/.1i 1=k/.1i k.i=1C i//, a decreasing function of the interest i (for all reasonable values of i ). For some applications, realistic values of interest rates result in relatively low competitive ratios. By using randomization the on-line player can further boost up the performance. In particular, against an oblivious adversary the on-line player can attain a strictly smaller compet- itive ratio of 2i..k=.ki 1// ∞ i 2/=..k=.ki 1// ∞ i 1/ where∞D ln.1i k.1i 1=.1C i///=ln.1=.1C i//. Here again, this competitive ratio strictly decreases with i . We also study the leasing problem against a distributional adversary called "Nature." This adversary chooses the probability distribution of the number of leasing periods and announces this distribution before the on-line player chooses a strategy. Although at the outset this adversary appears to be weaker than the oblivious adversary, it is shown that the optimal competitive ratio against Nature equals the optimal ratio against the oblivious adversary.

On randomization in on-line computation

Abstract: This paper concerns two fundamental but somewhat neglected issues, both related to the design and analysis of randomized on-line algorithms. Motivated by early results in game theory we define several types of randomized on-line algorithms, discuss known conditions for their equivalence, and give a natural example distinguishing between two kinds of randomizations. In particular, we show thatmixedrandomized memoryless paging algorithms can achieve strictly better competitive performance thanbehavioralrandomized algorithms. Next we summarize known—and derive new—“Yao principle” theorems for lower bounding competitive ratios of randomized on-line algorithms. This leads to four different theorems for bounded/unbounded and minimization/maximization problems.