On Randomization in On-Line Computation

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.