## Bounded Ordered Dictionaries in O(log log N) Time and O(n) Space (1990)

Venue: | Information Processing Letters |

Citations: | 14 - 0 self |

### BibTeX

@ARTICLE{Mehlhorn90boundedordered,

author = {Kurt Mehlhorn and Stefan Näher},

title = {Bounded Ordered Dictionaries in O(log log N) Time and O(n) Space},

journal = {Information Processing Letters},

year = {1990},

volume = {35}

}

### OpenURL

### Abstract

In this paper we show how to implement bounded ordered dictionaries, also called bounded priority queues, in O(log log N) time per operation and O(n) space. Here n denotes the number of elements stored in the dictionary and N denotes the size of the universe. Previously, this time bound required O(N) space [E77].

### Citations

87 |
Log-logarithmic worst-case range queries are possible in space theta(n
- Willard
- 1983
(Show Context)
Citation Context ...], and [J82] it is shown that the time bounds can be achieved using O(N) space and that a space bound O(N ffl ) can be achieved at the cost of multiplying the time bounds by 1=ffl for any ffl ? 0. In =-=[W83]-=- the space bound O(jdom Dj) is achieved for static dictionaries, and in [K84], [W84] the space O(jdom Dj) and an O( p log N) time bound is achieved. Many applications of dictionaries require insertion... |

48 | Data Structures and Algorithms - Mehlhorn - 1984 |

44 |
priority queue in which initialization and queue operations take o(loglogd) time
- Johnson, “A
- 1982
(Show Context)
Citation Context ...by the algorithm and not over the input sequence. q.e.d. This result extends and unifies the work of v. Emde Boas et al., v. Emde Boas, D. Johnson, R. Karlsson, and D. Willard. In [E77], [EKZ77], and =-=[J82]-=- it is shown that the time bounds can be achieved using O(N) space and that a space bound O(N ffl ) can be achieved at the cost of multiplying the time bounds by 1=ffl for any ffl ? 0. In [W83] the sp... |

26 |
New trie data structures which support very fast search operations
- Willard
- 1984
(Show Context)
Citation Context ...hat a space bound O(N ffl ) can be achieved at the cost of multiplying the time bounds by 1=ffl for any ffl ? 0. In [W83] the space bound O(jdom Dj) is achieved for static dictionaries, and in [K84], =-=[W84]-=- the space O(jdom Dj) and an O( p log N) time bound is achieved. Many applications of dictionaries require insertions and deletions but cannot afford O(N) storage. For these applications we improve th... |

14 |
Algorithms in a restricted universe
- Karlsson
- 1984
(Show Context)
Citation Context ...e and that a space bound O(N ffl ) can be achieved at the cost of multiplying the time bounds by 1=ffl for any ffl ? 0. In [W83] the space bound O(jdom Dj) is achieved for static dictionaries, and in =-=[K84]-=-, [W84] the space O(jdom Dj) and an O( p log N) time bound is achieved. Many applications of dictionaries require insertions and deletions but cannot afford O(N) storage. For these applications we imp... |

1 |
Tarjan: "Upper and Lower Bounds for the Dictionary Problem
- Dietzfelbinger, Karlin, et al.
- 1988
(Show Context)
Citation Context ...ctionaries, i.e. of partial functions on [0 : : : N \Gamma 1] with operations init; insert; delete; lookup and defined, which supports all five operations in time O(1). We use dynamic perfect hashing =-=[DKMMRT88]-=- instead of arrays. Fact ([DKMMRT88]) : For prime N , dynamic perfect hashing realizes bounded dictionaries in constant time per operation. The time bound for init; lookup and defined is worst case, t... |

1 | Emde Boas: "An O(n log log n) On-line Algorithm for the InsertExtract -Min Problem", Rep - v - 1974 |

1 |
Emde Boas: "Preserving Order in a Forest in Less than Logarithmic Time and Linear Space
- v
- 1977
(Show Context)
Citation Context ... O(log log N) time per operation and O(n) space. Here n denotes the number of elements stored in the dictionary and N denotes the size of the universe. Previously, this time bound required O(N) space =-=[E77]-=-. 1 I. Introduction A bounded ordered dictionary D on [0 : : : N \Gamma1] is a partial function from [0 : : : N \Gamma 1] to some set I, called the information type of D, together with the following o... |

1 |
Zijlstra: "Design and Implementation of an Efficient Priority Queue
- Boas, Kaas, et al.
(Show Context)
Citation Context ...choices made by the algorithm and not over the input sequence. q.e.d. This result extends and unifies the work of v. Emde Boas et al., v. Emde Boas, D. Johnson, R. Karlsson, and D. Willard. In [E77], =-=[EKZ77]-=-, and [J82] it is shown that the time bounds can be achieved using O(N) space and that a space bound O(N ffl ) can be achieved at the cost of multiplying the time bounds by 1=ffl for any ffl ? 0. In [... |

1 |
Szemeredi: "Storing a Sparse Table with O(1) Worst Case Access Time
- Fredman, Komlos, et al.
- 1984
(Show Context)
Citation Context ... use O(n) space. The model of computation is the unit-cost RAM where the arithmetic operations +; \Gamma; , mod, div on integers of value at most N take unit time. For more details see [DKMMRT88] and =-=[FKS84]-=-. q.e.d. This paper is organized as follows. In section II we prove the theorem above. Section III contains the complete programs. They are written in C++ and are part of the LEDA library [MN89]. Sect... |

1 |
Naher: "LEDA, a Library of Efficient Data Types and Algorithms
- Mehlhorn, St
- 1989
(Show Context)
Citation Context ... and [FKS84]. q.e.d. This paper is organized as follows. In section II we prove the theorem above. Section III contains the complete programs. They are written in C++ and are part of the LEDA library =-=[MN89]-=-. Section IV offers a short conclusion. II. The Construction A bounded ordered dictionary D on [0 : : : N \Gamma 1]; N prime, is realized by a data structure consisting of four parts: the integer N , ... |