On randomization in online computation

This paper concerns two fundamental but somewhat neglected issues both related to the design and analysis of randomized online algorithms. Motivated by early results in game theory we define several types of randomized online algorithms discuss known conditions for their equivalence and give a natural example distinguishing between two kinds of randomizations. In particular we show that mixed randomized memoryless paging algorithms can achieve strictly better competitive performance than behavioral randomized algorithms. Next we summarize known-and derive new-"Yao Principle" theorems for lower bounding competitive ratios of randomized online algorithms. This leads to six different theorems for bounded/unbounded and minimization/maximization problems.