Topic
Pairing heap
About: Pairing heap is a research topic. Over the lifetime, 65 publications have been published within this topic receiving 4095 citations.
Papers published on a yearly basis
Papers
TL;DR: Using F-heaps, a new data structure for implementing heaps that extends the binomial queues proposed by Vuillemin and studied further by Brown, the improved bound for minimum spanning trees is the most striking.
Abstract: In this paper we develop a new data structure for implementing heaps (priority queues). Our structure, Fibonacci heaps (abbreviated F-heaps), extends the binomial queues proposed by Vuillemin and studied further by Brown. F-heaps support arbitrary deletion from an n-item heap in O(log n) amortized time and all other standard heap operations in O(1) amortized time. Using F-heaps we are able to obtain improved running times for several network optimization algorithms. In particular, we obtain the following worst-case bounds, where n is the number of vertices and m the number of edges in the problem graph: O(n log n + m) for the single-source shortest path problem with nonnegative edge lengths, improved from O(mlog(m/n+2)n);O(n2log n + nm) for the all-pairs shortest path problem, improved from O(nm log(m/n+2)n);O(n2log n + nm) for the assignment problem (weighted bipartite matching), improved from O(nmlog(m/n+2)n);O(mβ(m, n)) for the minimum spanning tree problem, improved from O(mlog log(m/n+2)n); where β(m, n) = min {i | log(i)n ≤ m/n}. Note that β(m, n) ≤ log*n if m ≥ n.Of these results, the improved bound for minimum spanning trees is the most striking, although all the results give asymptotic improvements for graphs of appropriate densities.
3,081 citations
TL;DR: A new form of heap is described, intended to be competitive with the Fibonacci heap in theory and easy to implement and fast in practice, and a partial complexity analysis of pairing heaps is provided.
Abstract: Recently, Fredman and Tarjan invented a new, especially efficient form of heap (priority queue) called theFibonacci heap. Although theoretically efficient, Fibonacci heaps are complicated to implement and not as fast in practice as other kinds of heaps. In this paper we describe a new form of heap, called thepairing heap, intended to be competitive with the Fibonacci heap in theory and easy to implement and fast in practice. We provide a partial complexity analysis of pairing heaps. Complete analysis remains an open problem.
302 citations
TL;DR: The relaxed heap is a priority queue data structure that achieves the same amortized time bounds as the Fibonacci heap—a sequence of m decrease_key and n delete_min operations takes time O(m + n log n).
Abstract: The relaxed heap is a priority queue data structure that achieves the same amortized time bounds as the Fibonacci heap—a sequence of m decrease_key and n delete_min operations takes time O(m + n log n). A variant of relaxed heaps achieves similar bounds in the worst case—O(1) time for decrease_key and O(log n) for delete_min. Relaxed heaps give a processor-efficient parallel implementation of Dijkstra's shortest path algorithm, and hence other algorithms in network optimization. A relaxed heap is a type of binomial queue that allows heap order to be violated.
235 citations
TL;DR: The proposed structure, called a min-max heap, can be built in linear time and can be generalized to support other similar order-statistics operations efficiently (e.g., constant time and logarithmic time).
Abstract: A simple implementation of double-ended priority queues is presented The proposed structure, called a min-max heap, can be built in linear time; in contrast to conventional heaps, it allows both FindMin and FindMax to be performed in constant time; Insert, DeleteMin, and DeleteMax operations can be performed in logarithmic timeMin-max heaps can be generalized to support other similar order-statistics operations efficiently (eg, constant time FindMedian and logarithmic time DeleteMedian); furthermore, the notion of min-max ordering can be extended to other heap-ordered structures, such as leftist trees
183 citations
5 Jul 2000
TL;DR: It is shown that pairing heaps have a distribution sensitive behavior whereby the cost to perform an extract-min on an element x is O(log min(n, k) where k is the number of heap operations performed since x's insertion.
Abstract: Pairing heaps are shown to have constant amortized time insert and zero amortized time meld, thus improving the previous O(log n) amortized time bound on these operations. It is also shown that pairing heaps have a distribution sensitive behavior whereby the cost to perform an extract-min on an element x is O(log min(n, k)) where k is the number of heap operations performed since x's insertion. Fredman has observed that pairing heaps can be used to merge sorted lists of varying sized optimally, within constant factors. Utilizing the distribution sensitive behavior of pairing heap, an alternative method the employs pairing heaps for optimal list merging is derived.
98 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2020 | 1 |
| 2018 | 5 |
| 2017 | 3 |
| 2016 | 3 |
| 2015 | 2 |