Top-Down Skiplists

We describe todolists (top-down skiplists), a variant of skiplists (Pugh 1990) that can execute searches using at most log2−εn +O(1) binary comparisons per search and that have amortized update timeO(ε−1 logn). A variant of todolists, called working-todolists, can execute a search for any element x using log2−εw(x)+ o(logw(x)) binary comparisons and have amortized search time O(ε−1 logw(w)). Here, w(x) is the “working-set number” of x. No previous data structure is known to achieve a bound better than 4log2w(x) comparisons. We show through experiments that, if implemented carefully, todolists are comparable to other common dictionary implementations in terms of insertion times and outperform them in terms of search times. ∗School of Computer Science, Carleton University and Département d’Informatique, Université Libre de Bruxelles, [email protected] †School of Computer Science, Carleton University, [email protected] ar X iv :1 40 7. 79 17 v1 [ cs .D S] 3 0 Ju l 2 01 4