Dynamic online multiselection in internal and external memory

Abstract

We consider the dynamic version of the online multiselection problem for internal and external memory, in which q selection queries are requested on an unsorted array of N elements. Our internal memory result is 1-competitive with the offline result of Kaligosi et al.[ICALP 2005]. In particular, we extend the results of Barbary et al.[ESA 2013] by supporting arbitrary insertions and deletions while supporting online select and search queries on the array. Assuming that the insertion of an element is immediately preceded by a search for that element, we show that our dynamic online algorithm performs an optimal number of comparisons, up to lower order terms and an additive O(N) term. For the external memory model, we describe the first online multiselection algorithm that is O(1)-competitive. This result improves upon the work of Sibeyn [Journal of Algorithms 2006] when q >m, where m is the number of blocks that can be stored in main memory. We also extend it to support searches, insertions, and deletions of elements efficiently.