### Citations

2385 | A note on two problems in connexion with graphs
- Dijkstra
- 1959
(Show Context)
Citation Context ...tice [2]. Fredman and Tarjan [11] invented the Fibonacci heap specifically to support key decrease operations in O(1) time, which allows efficient implementation of Dijkstra’s shortest path algorithm =-=[3, 11]-=-, Edmonds’ minimum branching algorithm [6, 13], and certain minimum spanning tree algorithms [11, 13]. Fibonacci heaps support deletion of the minimum or of an arbitrary item in O(log n) amortized tim... |

900 | The art of computer programming. Volume 3. Sorting and Searching - Knuth - 1973 |

739 | Fibonacci heaps and their uses in improved network optimization algorithms
- Fredman, Tarjan
- 1987
(Show Context)
Citation Context ...ed to our work. The binomial queue of Vuillemin [29] supports all the heap operations in O(log n) worst-case time per operation. This structure performs quite well in practice [2]. Fredman and Tarjan =-=[11]-=- invented the Fibonacci heap specifically to support key decrease operations in O(1) time, which allows efficient implementation of Dijkstra’s shortest path algorithm [3, 11], Edmonds’ minimum branchi... |

667 |
Data structures and network algorithms
- Tarjan
- 1983
(Show Context)
Citation Context ...tion of a heap. (See Figure 1c.) In the half-ordered representation we do not need to move items among nodes as matches take place, so the items can be the nodes: the data structure can be endogenous =-=[27]-=-. Henceforth we shall assume an endogenous representation. We obtain our fourth and final representation, the heap-ordered representation, by viewing a half tree as the binary tree representation of a... |

426 |
The Art of Computer Programming, Volume 1 (Fundamental Algorithms), 2nd Edition
- Knuth
- 1973
(Show Context)
Citation Context ...lly presented in the heap-ordered representation. In their paper on pairing heaps, Fredman et al. [10] described the half-ordered representation and observed that it is the binary tree representation =-=[20]-=- of a heap-ordered tree. Later, Dutton [5] used the half-ordered representation in his weak-heap data structure, and Høyer [15] proposed various kinds of half-ordered balanced trees as heaps. The vers... |

189 |
Trans-dichotomous algorithms for minimum spanning trees and shortest paths.
- Fredman, Willard
- 1994
(Show Context)
Citation Context ...) amortized time, and each of the other supported heap operations takes O(1) amortized time. These bounds match the lower bound. (The logarithmic lower bound can be beaten by using multiway branching =-=[12, 14]-=-.) Many heap implementations have been proposed over the years. See e.g. [19]. We mention only those directly related to our work. The binomial queue of Vuillemin [29] supports all the heap operations... |

166 |
Amortized Computational Complexity.
- Tarjan
- 1985
(Show Context)
Citation Context ...g x. We shall assume that all keys are distinct; if they are not, we can break ties using any total order of the items. We allow only binary comparisons of keys, and we study the amortized efficiency =-=[28]-=- of heap operations. To obtain a bound on amortized efficiency, we assign to each configuration of the data structure a non-negative potential, initially zero. We define the amortized time of an opera... |

117 |
Efficient algorithms for finding minimum spanning trees in undirected and directed graphs. Combinatorica
- Gabow, Galil, et al.
- 1986
(Show Context)
Citation Context ... Fibonacci heap specifically to support key decrease operations in O(1) time, which allows efficient implementation of Dijkstra’s shortest path algorithm [3, 11], Edmonds’ minimum branching algorithm =-=[6, 13]-=-, and certain minimum spanning tree algorithms [11, 13]. Fibonacci heaps support deletion of the minimum or of an arbitrary item in O(log n) amortized time and the other heap operations in O(1) amorti... |

103 | A Data Structure for Manipulating Priority Queues
- Vuillemin
- 1978
(Show Context)
Citation Context ... by using multiway branching [12, 14].) Many heap implementations have been proposed over the years. See e.g. [19]. We mention only those directly related to our work. The binomial queue of Vuillemin =-=[29]-=- supports all the heap operations in O(log n) worst-case time per operation. This structure performs quite well in practice [2]. Fredman and Tarjan [11] invented the Fibonacci heap specifically to sup... |

95 |
An empirical comparison of priority-queue and event-set implementations
- Jones
- 1986
(Show Context)
Citation Context ...10]. Pairing heaps support all the heap operations in O(log n) amortized time and were conjectured to support key decrease in O(1) amortized time. Despite empirical evidence supporting the conjecture =-=[16, 22, 26]-=-, Fredman [9] showed that it is not true: pairing heaps and related data structures that do not store subtree size information require Ω(log log n) amortized time per key decrease. Whether pairing hea... |

85 |
Relaxed heaps: An alternative to Fibonacci heaps with applications to parallel computation
- Driscoll, Gabow, et al.
- 1988
(Show Context)
Citation Context ...ortized time and the other heap operations in O(1) amortized time. They do not perform well in practice, however [22, 23]. As a result, a variety of alternatives to Fibonacci heaps have been proposed =-=[4, 7, 15, 18, 19, 24]-=-, including a self-adjusting structure, the pairing heap [10]. Pairing heaps support all the heap operations in O(log n) amortized time and were conjectured to support key decrease in O(1) amortized t... |

59 |
The Pairing Heap: A New Form of Self-adjusting Heap,
- Fredman, Sedgewick, et al.
- 1986
(Show Context)
Citation Context ...perform well in practice, however [22, 23]. As a result, a variety of alternatives to Fibonacci heaps have been proposed [4, 7, 15, 18, 19, 24], including a self-adjusting structure, the pairing heap =-=[10]-=-. Pairing heaps support all the heap operations in O(log n) amortized time and were conjectured to support key decrease in O(1) amortized time. Despite empirical evidence supporting the conjecture [16... |

50 |
Implementation and analysis of binomial queue algorithms
- Brown
- 1978
(Show Context)
Citation Context ...nly those directly related to our work. The binomial queue of Vuillemin [29] supports all the heap operations in O(log n) worst-case time per operation. This structure performs quite well in practice =-=[2]-=-. Fredman and Tarjan [11] invented the Fibonacci heap specifically to support key decrease operations in O(1) time, which allows efficient implementation of Dijkstra’s shortest path algorithm [3, 11],... |

39 |
Pairing heaps: experiments and analysis
- Stasko, Vitter
- 1987
(Show Context)
Citation Context ...10]. Pairing heaps support all the heap operations in O(log n) amortized time and were conjectured to support key decrease in O(1) amortized time. Despite empirical evidence supporting the conjecture =-=[16, 22, 26]-=-, Fredman [9] showed that it is not true: pairing heaps and related data structures that do not store subtree size information require Ω(log log n) amortized time per key decrease. Whether pairing hea... |

33 | Worst-case efficient priority queues
- Brodal
- 1996
(Show Context)
Citation Context ...ing the data structure more complicated: run-relaxed heaps [4] and fat heaps [18] achieve these bounds except for melding, which takes O(log n) time worst-case; a very complicated structure of Brodal =-=[1]-=- achieves these bounds for all the heap operations. Our goal is to systematically explore the design space of amortized-efficient heaps and thereby discover the simplest possible data structures. As a... |

32 | Integer sorting in O(n √ log log n) expected time and linear space
- Han, Thorup
- 2012
(Show Context)
Citation Context ...) amortized time, and each of the other supported heap operations takes O(1) amortized time. These bounds match the lower bound. (The logarithmic lower bound can be beaten by using multiway branching =-=[12, 14]-=-.) Many heap implementations have been proposed over the years. See e.g. [19]. We mention only those directly related to our work. The binomial queue of Vuillemin [29] supports all the heap operations... |

26 | An Empirical Analysis of Algorithms for Constructing a Minimum Spanning Tree,
- Moret, Shapiro
- 1991
(Show Context)
Citation Context ... Fibonacci heaps support deletion of the minimum or of an arbitrary item in O(log n) amortized time and the other heap operations in O(1) amortized time. They do not perform well in practice, however =-=[22, 23]-=-. As a result, a variety of alternatives to Fibonacci heaps have been proposed [4, 7, 15, 18, 19, 24], including a self-adjusting structure, the pairing heap [10]. Pairing heaps support all the heap o... |

21 |
On the Efficiency of Pairing Heaps and Related Data Structures,
- Fredman
- 1999
(Show Context)
Citation Context ...port all the heap operations in O(log n) amortized time and were conjectured to support key decrease in O(1) amortized time. Despite empirical evidence supporting the conjecture [16, 22, 26], Fredman =-=[9]-=- showed that it is not true: pairing heaps and related data structures that do not store subtree size information require Ω(log log n) amortized time per key decrease. Whether pairing heaps meet this ... |

21 |
Meldable heaps and boolean union-find
- Kaplan, Shafrir, et al.
- 2002
(Show Context)
Citation Context ...and melds occur, one needs a separate data structure to maintain the partition of items into heaps. With such a data structure, the time to find the heap containing a given item is small but not O(1) =-=[17]-=-. Fibonacci heaps [11] were invented specifically to support key decrease efficiently, but they require two extra pointers per node (in the heap-ordered representation, to the parent and previous sibl... |

18 | Towards a Final Analysis of Pairing Heaps
- Pettie
- 2005
(Show Context)
Citation Context ... data structures that do not store subtree size information require Ω(log log n) amortized time per key decrease. Whether pairing heaps meet this bound is open; the best upper bound is O(22 √ lg lgn) =-=[25]-=-5. Very recently ElMasry [8] proposed a more-complicated alternative to pairing heaps that does have an O(log log n) amortized bound per key decrease. Fredman’s result gives a time-space trade-off bet... |

17 |
A balanced tree scheme for meldable heaps with updates
- Peterson
- 1987
(Show Context)
Citation Context ...ortized time and the other heap operations in O(1) amortized time. They do not perform well in practice, however [22, 23]. As a result, a variety of alternatives to Fibonacci heaps have been proposed =-=[4, 7, 15, 18, 19, 24]-=-, including a self-adjusting structure, the pairing heap [10]. Pairing heaps support all the heap operations in O(log n) amortized time and were conjectured to support key decrease in O(1) amortized t... |

13 |
New Heap Data Structures
- Kaplan, Tarjan
- 1999
(Show Context)
Citation Context ...ortized time and the other heap operations in O(1) amortized time. They do not perform well in practice, however [22, 23]. As a result, a variety of alternatives to Fibonacci heaps have been proposed =-=[4, 7, 15, 18, 19, 24]-=-, including a self-adjusting structure, the pairing heap [10]. Pairing heaps support all the heap operations in O(log n) amortized time and were conjectured to support key decrease in O(1) amortized t... |

13 |
Three priority queue applications revisited
- Liao
- 1992
(Show Context)
Citation Context ... Fibonacci heaps support deletion of the minimum or of an arbitrary item in O(log n) amortized time and the other heap operations in O(1) amortized time. They do not perform well in practice, however =-=[22, 23]-=-. As a result, a variety of alternatives to Fibonacci heaps have been proposed [4, 7, 15, 18, 19, 24], including a self-adjusting structure, the pairing heap [10]. Pairing heaps support all the heap o... |

12 | A general technique for implementation of efficient priority queues
- Høyer
- 1995
(Show Context)
Citation Context |

9 | Thin heaps, thick heaps
- Kaplan, Tarjan
(Show Context)
Citation Context ...tized time. These bounds match the lower bound. (The logarithmic lower bound can be beaten by using multiway branching [12, 14].) Many heap implementations have been proposed over the years. See e.g. =-=[19]-=-. We mention only those directly related to our work. The binomial queue of Vuillemin [29] supports all the heap operations in O(log n) worst-case time per operation. This structure performs quite wel... |

7 |
The weak-heap data structure
- Dutton
(Show Context)
Citation Context ...ation. In their paper on pairing heaps, Fredman et al. [10] described the half-ordered representation and observed that it is the binary tree representation [20] of a heap-ordered tree. Later, Dutton =-=[5]-=- used the half-ordered representation in his weak-heap data structure, and Høyer [15] proposed various kinds of half-ordered balanced trees as heaps. The version of Fredman et al. [10] matches Knuth’s... |

3 | Violation heaps: A better substitute for fibonacci heaps
- Elmasry
(Show Context)
Citation Context |

1 |
Pairing heaps with O(log logn) decrease cost
- Elmasry
- 2009
(Show Context)
Citation Context ...store subtree size information require Ω(log log n) amortized time per key decrease. Whether pairing heaps meet this bound is open; the best upper bound is O(22 √ lg lgn) [25]5. Very recently ElMasry =-=[8]-=- proposed a more-complicated alternative to pairing heaps that does have an O(log log n) amortized bound per key decrease. Fredman’s result gives a time-space trade-off between the number of bits per ... |