## A New Trade-off for Deterministic Dictionaries (2000)

### Cached

### Download Links

- [www.brics.dk]
- [www.it-c.dk]
- [www.itu.dk]
- DBLP

### Other Repositories/Bibliography

Citations: | 1 - 0 self |

### BibTeX

@MISC{Pagh00anew,

author = {Rasmus Pagh},

title = {A New Trade-off for Deterministic Dictionaries},

year = {2000}

}

### OpenURL

### Abstract

. We consider dictionaries over the universe U = f0; 1g w on a unit-cost RAM with word size w and a standard instruction set. We present a linear space deterministic dictionary with membership queries in time (log log n) O(1) and updates in time (log n) O(1) , where n is the size of the set stored. This is the rst such data structure to simultaneously achieve query time (log n) o(1) and update time O(2 (log n) c ) for a constant c < 1. 1 Introduction Among the most fundamental data structures is the dictionary. A dictionary stores a subset S of a universe U , oering membership queries of the form \x 2 S?". The result of a membership query is either 'no' or a piece of satellite data associated with x. Updates of the set are supported via insertion and deletion of single elements. Several performance measures are of interest for dictionaries: The amount of space used, the time needed to answer queries, and the time needed to perform updates. The most ecient dictionar...

### Citations

246 | Making data structures persistent
- Driscoll, Sarnak, et al.
- 1989
(Show Context)
Citation Context ... Since we need associated element lists of length Ω((log n) 2 ), we cannot afford to use sorted lists as before (updates would become more expensive). Instead, we use persistent balanced search trees =-=[6]-=-, which support updates and queries in time O(log t) for a sequence of trees of size at most t. One technicality is that many instances of the algorithm finding distinguishing bits have to run at the ... |

137 | Should tables be sorted
- Yao
- 1981
(Show Context)
Citation Context ...ur construction. An unpublished manuscript by Sundar [13] states an amortized lower bound of time Ω( log logw n log log logw n ) per operation for a deterministic dictionary in Yao’s cell probe model =-=[15]-=-, which in particular implies the same lower bound on the word RAM. Note that for w = (log n) O(1) , the BFAT data structure has time perslog n log log n update n [12] [13] [here] [1,2] 1 log log n lo... |

127 | Dynamic perfect hashing: Upper and lower bounds
- Dietzfelbinger, Karlin, et al.
- 1988
(Show Context)
Citation Context ...tant from a theoretical point of view. All this has led to an interest in derandomization of known randomized algorithms and data structures. Several recent papers consider deterministic dictionaries =-=[4, 10, 11, 12, 13]-=-. However, previous space-efficient dictionaries with very fast lookups (time (log n) o(1) ) have had update time much larger than that of, say, binary search trees. Therefore these dictionaries are o... |

86 |
Preserving order in a forest in less than logarithmic time
- Boas
- 1975
(Show Context)
Citation Context ...ng another strategy, in which there are Θ(log n) sets of each size, and only O(log n/ log log n) different set sizes. If the requirement of linear space is abandoned, substituting van Emde Boas trees =-=[14]-=- for the BFAT data structure gives membership queries in time O(log log n). The space usage then rises to n O(log n) . It can be noted that the predecessor data structure is used in such a way that it... |

62 | Optimal bounds for the predecessor problem
- Beame, Fich
- 1999
(Show Context)
Citation Context ...he situation where update and query time are considered equally important, is O( � log n/ log log n) time per dictionary operation. It is a dynamization of the static data structure of Beame and Fich =-=[2]-=- using the exponential search trees of Andersson and Thorup [1]. The Beame-Fich-Andersson-Thorup (BFAT) data structure in fact supports predecessor queries of the form “What is the largest element of ... |

43 |
Sorting and searching on the word RAM
- Hagerup
(Show Context)
Citation Context ...t-cost word RAM, in which each memory register contains a w-bit integer (a word). This model of computation, resembling modern computers, has been the object of much recent research. Hagerup’s survey =-=[9]-=- contains a description of the model. We adopt the multiplication model whose instruction set includes addition, bitwise boolean operations, shifts and multiplication. Note that all operations can als... |

40 | Tight(er) worst-case bounds on dynamic searching and priority queues
- Andersson, Thorup
- 2000
(Show Context)
Citation Context ... important, is O( � log n/ log log n) time per dictionary operation. It is a dynamization of the static data structure of Beame and Fich [2] using the exponential search trees of Andersson and Thorup =-=[1]-=-. The Beame-Fich-Andersson-Thorup (BFAT) data structure in fact supports predecessor queries of the form “What is the largest element of S not greater than x?”. Its time bound improves significantly i... |

38 |
János Komlós, and Endre Szemerédi. Storing a sparse table with O(1) worst case access time
- Fredman
- 1984
(Show Context)
Citation Context ... bounds will be independent of w, unless explicitly stated. Note that the optimal space consumption of a dictionary is Θ(n) words. 1.1 Related Work The seminal result of Fredman, Komlós and Szemerédi =-=[7]-=- is that a static dictionary (i.e. without update operations) can have constant query time and linear space consumption. Allowing randomization, the FKS static dictionary can be made dynamic, supporti... |

27 |
Polynomial hash functions are reliable (extended abstract
- Dietzfelbinger, Gil, et al.
(Show Context)
Citation Context ...erations are done in constant time with high probability (i.e. probability at least 1 − n−c , where c is any constant of our choice). A simpler dictionary with the same properties was later developed =-=[3]-=-. As for randomized dictionaries, this leaves very little to be improved. Without a source of random bits, the task of simultaneously achieving fast updates and constant query time seems considerably ... |

22 | Friedhelm Meyer auf der - Dietzfelbinger, Karlin, et al. - 1990 |

21 | Endre Szemeredi. Storing a sparse table with O(1) worst case access time - Fredman, Komlos - 1984 |

17 | Error correcting codes, perfect hashing circuits, and deterministic dynamic dictionaries
- Miltersen
- 1998
(Show Context)
Citation Context ...tant from a theoretical point of view. All this has led to an interest in derandomization of known randomized algorithms and data structures. Several recent papers consider deterministic dictionaries =-=[4, 10, 11, 12, 13]-=-. However, previous space-efficient dictionaries with very fast lookups (time (log n) o(1) ) have had update time much larger than that of, say, binary search trees. Therefore these dictionaries are o... |

15 |
Friedhelm Meyer auf der Heide. A new universal class of hash functions and dynamic hashing in real time
- Dietzfelbinger
- 1990
(Show Context)
Citation Context ...owing randomization, the FKS static dictionary can be made dynamic, supporting insertions and deletions in amortized expected constant time [4]. Improving this, Dietzfelbinger and Meyer auf der Heide =-=[5]-=- have constructed a dictionary in which all operations are done in constant time with high probability (i.e. probability at least 1 − n−c , where c is any constant of our choice). A simpler dictionary... |

13 | Surpassing the information-theoretic bound with fusion trees - Fredman, Willard - 1993 |

9 | Faster deterministic dictionaries
- Pagh
- 2000
(Show Context)
Citation Context ...tant from a theoretical point of view. All this has led to an interest in derandomization of known randomized algorithms and data structures. Several recent papers consider deterministic dictionaries =-=[4, 10, 11, 12, 13]-=-. However, previous space-efficient dictionaries with very fast lookups (time (log n) o(1) ) have had update time much larger than that of, say, binary search trees. Therefore these dictionaries are o... |

8 |
A lower bound on the cell probe complexity of the dictionary problem. Unpublished manuscript
- Sundar
- 1993
(Show Context)
Citation Context |

5 |
Fast deterministic construction of static dictionaries
- Hagerup
- 1999
(Show Context)
Citation Context |