Topic
Brodal queue
About: Brodal queue is a research topic. Over the lifetime, 6 publications have been published within this topic receiving 62 citations.
Papers
TL;DR: This paper adapts Brodal's data structure to a purely functional setting and clarifies its relationship to the binomial queues of Vuillemin, which support all four operations in O(log n) time.
Abstract: Brodal recently introduced the first implementation of imperative priority queues to support findMin, insert, and meld in O(1) worst-case time, and deleteMin in O(log n) worst-case time. These bounds are asymptotically optimal among all comparison-based priority queues. In this paper, we adapt Brodal's data structure to a purely functional setting. In doing so, we both simplify the data structure and clarify its relationship to the binomial queues of Vuillemin, which support all four operations in O(log n) time. Specifically, we derive our implementation from binomial queues in three steps: first, we reduce the running time of insert to O(1) by eliminating the possibility of cascading links; second, we reduce the running time of findMin to O(1) by adding a global root to hold the minimum element; and finally, we reduce the running time of meld to O(1) by allowing priority queues to contain other priority queues. Each of these steps is expressed using ML-style functors. The last transformation, known as data-structural bootstrapping, is an interesting application of higher-order functors and recursive structures.
41 citations
TL;DR: It is demonstrated how an unconventional, but practically implementable, memory architecture can be employed to sidestep a lower bound and achieve constant time performance.
32 citations
3 Jul 2012
TL;DR: A new variant of the worst-case efficient priority queues that relies on extended regular counters and provides the same asymptotic time and space bounds as the original is described.
Abstract: We consider the classical problem of representing a collection of priority queues under the operations find-min, insert, decrease, meld, delete, and delete-min. In the comparison-based model, if the first four operations are to be supported in constant time, the last two operations must take at least logarithmic time. Brodal showed that his worst-case efficient priority queues achieve these worst-case bounds. Unfortunately, this data structure is involved and the time bounds hide large constants. We describe a new variant of the worst-case efficient priority queues that relies on extended regular counters and provides the same asymptotic time and space bounds as the original. Due to the conceptual separation of the operations on regular counters and all other operations, our data structure is simpler and easier to describe and understand. Also, the constants in the time and space bounds are smaller.
8 citations
Proceedings Article•
3 Oct 1977
6 citations
11 Aug 1993
TL;DR: The basic form of the k-d heap uses no extra space, takes linear time to construct, and supports instant access to the items carrying the minimum key of any dimension, as well as logarithmic time insertion, deletion, and modification of any item in the queue.
Abstract: This paper presents the k-d heap, an efficient data structure that implements a multi-dimensional priority queue. The basic form of the k-d heap uses no extra space, takes linear time to construct, and supports instant access to the items carrying the minimum key of any dimension, as well as logarithmic time insertion, deletion, and modification of any item in the queue. Moreover, it can be extended to a multi-dimensional double-ended mergeable priority queue, capable of efficiently supporting all the operations linked to priority queues. The k-d heap is very easily implemented, and has direct applications.
4 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2019 | 1 |
| 2012 | 1 |
| 2005 | 1 |
| 1996 | 1 |
| 1993 | 1 |
| 1977 | 1 |