Biased Skip Lists 1

We design a variation of skip lists that performs well for generally biased access sequences. Given n items, each with a positive weight wi , 1 ≤ i ≤ n, the time to access item i is O(1 + log(W/wi )), where W =∑n i=1 wi ; the data structure is dynamic. We present two instantiations of biased skip lists, one of which achieves this bound in the worst case, the other in the expected case. The structures are nearly identical; the deterministic one simply ensures the balance condition that the randomized one achieves probabilistically. We use the same method to analyze both.