Theory and Implementation of Online Multiselection Algorithms

We introduce a new online algorithm for the multiselection problem which performs a sequence of selection queries on a given unsorted array. We show that our online algorithm is 1-competitive in terms of data comparisons. In particular, we match the bounds (up to lower order terms) from the optimal offline algorithm proposed by Kaligosi et al.[ICALP 2005]. We provide experimental results comparing online and offline algorithms. These experiments show that our online algorithms require fewer comparisons than the best-known offline algorithms. Interestingly, our experiments suggest that our optimal online algorithm (when used to sort the array) requires fewer comparisons than both quicksort and mergesort.