Worst-case efficient external-memory priority queues

Brodal, Gerth Stølting; Katajainen, Jyrki

doi:10.1007/bfb0054359

Cited by 68 publications

(94 citation statements)

References 16 publications

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“…After Dijkstra's result, most subsequent theoretical developments in SSSP for general graphs have focused on improving the performance of the priority queue: Applying William's heap [69] results in a running time of O(m · log n). Taking Fibonacci heaps [22] or similar data structures [4,17,64], Dijkstra's algorithm can be implemented to run in O(n · log n + m) time. In fact, if one sticks to Dijkstra's method, thus considering the nodes in nondecreasing order of distances, then O(n · log n + m) is even the best possible time bound for the comparisonaddition model: any o(n · log n)-time algorithm would contradict the Ω(n · log n)-time lower-bound for comparison-based sorting.…”

Section: Sequential Label-setting Algorithmsmentioning

confidence: 99%

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Average-case complexity of single-source shortest-paths algorithms: lower and upper bounds

Meyer

2003

Journal of Algorithms

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Section: Sequential Label-setting Algorithmsmentioning

confidence: 99%

“…If not, then the algorithms scan all nodes contained in B cur simultaneously; 4 we will denote this operation by SCAN_ALL(B cur ). We call this step of the algorithm regular node scanning.…”

Section: The Common Frameworkmentioning

confidence: 99%

Average-case complexity of single-source shortest-paths algorithms: lower and upper bounds

Meyer

2003

Journal of Algorithms

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“…There are many priority queue constructions that achieve this lower bound, such as the buffer tree [2], M/B-ary heaps [5], and array heaps [4]. See the survey [12] for more details.…”

Section: Related Workmentioning

confidence: 99%

Equivalence between Priority Queues and Sorting in External Memory

Wei¹,

Yi²

2014

Algorithms - ESA 2014

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Abstract.A priority queue is a fundamental data structure that maintains a dynamic ordered set of keys and supports the followig basic operations: insertion of a key, deletion of a key, and finding the smallest key. The complexity of the priority queue is closely related to that of sorting: A priority queue can be used to implement a sorting algorithm trivially. Thorup [11] proved that the converse is also true in the RAM model. In particular, he designed a priority queue that uses the sorting algorithm as a black box, such that the per-operation cost of the priority queue is asymptotically the same as the per-key cost of sorting. In this paper, we prove an analogous result in the external memory model, showing that priority queues are computationally equivalent to sorting in external memory, under some mild assumptions. The reduction provides a possibility for proving lower bounds for external sorting via showing a lower bound for priority queues.

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“…Note that if the key of an element to be updated is known (and assuming without loss of generality that all keys are distinct), the update can be performed in O((log m n)/B) I/Os using a deletion and an insertion. Other external priority queues are designed in [22] and [23].…”

Section: External Priority Queuementioning

confidence: 99%

The Buffer Tree: A Technique for Designing Batched External Data Structures

Arge¹

2003

Algorithmica

136

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Abstract. We present a technique for designing external memory data structures that support batched operations I/O efficiently. We show how the technique can be used to develop external versions of a search tree, a priority queue, and a segment tree, and give examples of how these structures can be used to develop I/Oefficient algorithms. The developed algorithms are either extremely simple or straightforward generalizations of known internal memory algorithms-given the developed external data structures.Key Words. I/O efficiency, Internal memory algorithms, Batched external data structures, Buffer tree. Introduction.In recent years, increasing attention has been given to Input/Outputefficient (or I/O-efficient) algorithms. This is due to the fact that communication between fast internal memory and slower external memory such as disks is the bottleneck in many computations involving massive datasets. The significance of this bottleneck is increasing as internal computation gets faster and parallel computing gains popularity.Much work has been done on designing external versions of data structures designed for internal memory. Most of these structures are designed to be used in on-line settings, where queries should be answered immediately and within a good worst case number of I/Os. As a consequence they often do not take advantage of the available main memory, leading to suboptimal performance when they are used in solutions for batched (or offline) problems. Therefore several techniques have been developed for solving massive batched problems without using external data structures.In this paper we present a technique for designing external data structures that take advantage of the large main memory. We do so by only requiring good amortized performance and by allowing query operations to be batched. We also show how the developed data structures can be used in simple and I/O-efficient algorithms for a number of fundamental computational geometry and graph problems. Our technique has subsequently been used in the development of a large number of I/O-efficient algorithms in these and several other problem areas.

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Worst-case efficient external-memory priority queues

Cited by 68 publications

References 16 publications

Average-case complexity of single-source shortest-paths algorithms: lower and upper bounds

Average-case complexity of single-source shortest-paths algorithms: lower and upper bounds

Equivalence between Priority Queues and Sorting in External Memory

The Buffer Tree: A Technique for Designing Batched External Data Structures

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