Median-of-k Jumplists and Dangling-Min BSTs

We extend randomized jumplists introduced by Brönnimann et al. (STACS 2003) to choose jump-pointer targets as median of a small sample for better search costs, and present randomized algorithms with expected O(log n) time complexity that maintain the probability distribution of jump pointers upon insertions and deletions. We analyze the expected costs to search, insert and delete a random element, and we show that omitting jump pointers in small sublists hardly affects search costs, but significantly reduces the memory consumption. We use a bijection between jumplists and "dangling-min BSTs", a variant of (fringe-balanced) binary search trees for the analysis. Despite their similarities, some standard analysis techniques for search trees fail for dangling-min trees (and hence for jumplists).