A Faster External Memory Priority Queue with DecreaseKeys

Abstract

A priority queue is a fundamental data structure that maintains a dynamic set of (key, priority)-pairs and supports Insert, Delete, ExtractMin and DecreaseKey operations. In the external memory model, the current best priority queue supports each operation in amortizedOs. If the DecreaseKey operation does not need to be supported, one can design a more efficient data structure that supports the Insert, Delete and ExtractMin operations in O( 1 B log N B / log M B ) I/Os. A recent result shows that a degradation in performance is inevitable by proving a lower bound of Ω( 1 B log B/ log log N ) I/Os for priority queues with DecreaseKeys. In this paper we tighten the gap between the lower bound and the upper bound by proposing a new priority queue which supports the DecreaseKey operation and has an expected amortized I/O complexity of O( 1 B log N B / log log N ). Our result improves the external memory priority queue with DecreaseKeys for the first time in over a decade, and also gives the fastest external memory single source shortest path algorithm.

Lower bounds for external memory integer sorting via network coding

“…Their lower bound improved over previous work by Yi and Zhang [19] and Verbin and Zhang [17]. In other very recent work, Jiang and Larsen [13] showed how to exploit integer input to develop external memory priority queues with DecreaseKeys that outperform their comparison based counterparts. Their upper bound almost matches an unconditional lower bound by Eenberg et al [6] (also proved in the cell probe model).…”

Re-Pair in Small Space

“…For realistic values of n, B, and M, we stipulate that scan(n) < sort(n) n. A simple approach is based on an EM heap maintaining the frequencies of all bigrams in the text. A state-of-the-art heap is due to Jiang and Larsen [39] This allows us to perform all sorting steps and binary searches in IM without additional I/O. We only trigger I/O operations for scanning the text, which is done n/d times, since we partition T into d substrings.…”

Cache-Oblivious Priority Queues with Decrease-Key and Applications to Graph Algorithms

“…Designing efficient external memory priority queues able to support operation DecreaseKey (or at least operation Update) has been a long-standing open problem [14,10,16,9,7,13]. I/Oefficient adaptations of the standard heap data structure [10] or other sorting-based approaches [16], despite achieving optimal base-(M/B) logarithmic amortized I/O-complexity, fail to support operation DecreaseKey.…”

“…Indeed, in the recent work of Eenberg, Larsen and Yu [9] it is shown that for a sequence of N operations, any external-memory priority queue supporting DecreaseKey must spend max{Insert, Delete, ExtractMin, DecreaseKey} = Ω 1 B log log N B amortized I/Os. Randomized priority queues with matching complexity were recently presented by Jiang and Larsen [13].…”