On Sorting, Heaps, and Minimum Spanning Trees.
Algorithmica, 57 (4):
585 - 620 (2010)Abstract
Let A be a set of size m. Obtaining the first k≤ m elements of A in ascending order can be done in optimal O( m+ klog k) time. We present Incremental Quicksort (IQS), an algorithm (online on k) which incrementally gives the next smallest element of the set, so that the first k elements are obtained in optimal expected time for any k. Based on IQS, we present the Quickheap (QH), a simple and efficient priority queue for main and secondary memory. Quickheaps are comparable with classical binary heaps in simplicity, yet are more cache-friendly. This makes them an excellent alternative for a secondary memory implementation. We show that the expected amortized CPU cost per operation over a Quickheap of m elements is O(log m), and this translates into O((1/ B)log ( m/ M)) I/O cost with main memory size M and block size B, in a cache-oblivious fashion. As a direct application, we use our techniques to implement classical Minimum Spanning Tree (MST) algorithms. We use IQS to implement Krusk
