## Fast Local Searches and Updates in Bounded Universes

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### BibTeX

@MISC{Bose_fastlocal,

author = {Prosenjit Bose and Karim Douïeb and Vida Dujmović and John Howat and Pat Morin},

title = {Fast Local Searches and Updates in Bounded Universes},

year = {}

}

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### Abstract

Given a bounded universe {0, 1,..., U −1}, we show how to perform (successor) searches in O(log log ∆) expected time and updates in O(log log ∆) expected amortized time, where ∆ is the rank difference between the element being searched for and its successor in the structure. This unifies the results of traditional bounded universe structures (which support successor searches in O(log log U) time) and hashing (which supports exact searches in O(1) time). We also show how these results can be extended to answer approximate nearest neighbour queries in low dimensions. 1

### Citations

337 | Lists: A probabilistic alternative to balanced trees, ommunications 31 (2008) 358–374 373been a member of over 40 international programme, scientific and conference committees. Dr Paul Sage received the degrees of B.Sc. Computer Science (Honours) and Ph.D
- Pugh, Skip
(Show Context)
Citation Context ...predecessor (in terms of priority) of the query. The idea of finger searching involves starting a search from somewhere inside a structure by supplying the search operation with a pointer. Skip lists =-=[10]-=- and finger search trees [3], for example, support finger searches in O(log δ) time, where δ is the rank distance between the given pointer and the query. On the RAM, Kaporis et al. [9] describe a dat... |

114 |
Emde Boas. Preserving order in a forest in less than logarithmic time and linear space
- van
- 1977
(Show Context)
Citation Context ...searching, however, return the element being searched for if it is present, or the successor of that element otherwise. Such searches can be supported in O(log log U) 1 time using van Emde Boas trees =-=[11]-=-, x-fast tries or y-fast tries [12]. We introduce the idea of local searching in a bounded universe in order to unify these two types of structures. Our goal is to execute successor searches in time O... |

86 |
Log-logarithmic worst-case range queries are possible in space theta(n
- Willard
- 1983
(Show Context)
Citation Context ...ent being searched for if it is present, or the successor of that element otherwise. Such searches can be supported in O(log log U) 1 time using van Emde Boas trees [11], x-fast tries or y-fast tries =-=[12]-=-. We introduce the idea of local searching in a bounded universe in order to unify these two types of structures. Our goal is to execute successor searches in time O(log log ∆), where ∆ is the rank di... |

44 |
priority queue in which initialization and queue operations take o(loglogd) time
- Johnson, “A
- 1982
(Show Context)
Citation Context ...can be performed in time O(log log U) using, for example, van Emde Boas trees [11] or y-fast tries [12]. Several results consider the distance between a query and an element in the structure. Johnson =-=[8]-=- describes a priority queue where insertion and deletion take time O(log log D), where D is the difference between the successor and predecessor (in terms of priority) of the query. The idea of finger... |

40 |
János Komlós, and Endre Szemerédi. Storing a sparse table with O(1) worst case access time
- Fredman
- 1984
(Show Context)
Citation Context ... low dimensions. 1 Introduction Let U = {0, 1, . . . , U − 1}. We address the problem of maintaining a dictionary subject to searches, insertions and deletions on a subset of U of size n. Hash tables =-=[6]-=- can support these operations in O(1) expected time per operation. Unfortunately, hash tables only work for exact searches; they do not provide a useful result for elements that are not stored in the ... |

34 | Closest-point problems simplified on the RAM
- Chan
(Show Context)
Citation Context ...or the query point, if it happens to be in the structure) in time O(log log ∆), where ∆ is the Euclidean distance to the point returned.22 nd Canadian Conference on Computational Geometry, 2010 Chan =-=[4]-=- points out that by placing d + 1 shifted versions of the stored points onto a space-filling curve2 , queries can be answered by answering the query on each of these curves (lists) and taking the clos... |

30 | Non-expansive hashing
- Linial, Sasson
- 1996
(Show Context)
Citation Context ...with O(1) worst-case update time and O(log log δ) expected search time for a large class of input distributions, where δ is the distance between the query and some finger. Locality preserving hashing =-=[9]-=- is a form of hashing that ensures that input values that are close together have hash values that are close together. For the temporal precedence problem, a list is maintained under insertions. Given... |

12 | Efficient regular data structures and algorithms for location and proximity problems
- Amir, Efrat, et al.
- 1999
(Show Context)
Citation Context ...e δ is temporal distance between the two given elements. In two or more dimensions, one concentrates on finding the (approximate) nearest neighbour of a query point. In bounded universes, Amir et al. =-=[1]-=- show how to answer queries and perform updates in expected time O(log log U). In unbounded universes, Derryberry et al. [5] describe a data structure that finds an approximate nearest neighbour p of ... |

6 |
Athanasios K. Tsakalidis, Kostas Tsichlas: Optimal finger search trees in the pointer machine
- Brodal, Lagogiannis, et al.
- 2003
(Show Context)
Citation Context ...rity) of the query. The idea of finger searching involves starting a search from somewhere inside a structure by supplying the search operation with a pointer. Skip lists [10] and finger search trees =-=[3]-=-, for example, support finger searches in O(log δ) time, where δ is the rank distance between the given pointer and the query. On the RAM, Kaporis et al. [9] describe a data structure with O(1) worst-... |

4 | Achieving spatial adaptivity while finding approximate nearest neighbors
- Derryberry, Sheehy, et al.
- 2008
(Show Context)
Citation Context ...mate) nearest neighbour of a query point. In bounded universes, Amir et al. [1] show how to answer queries and perform updates in expected time O(log log U). In unbounded universes, Derryberry et al. =-=[5]-=- describe a data structure that finds an approximate nearest neighbour p of the point q in some constant dimension in time O(log δ(p, q)), where δ(p, q) is the number of points in a certain box contai... |

2 |
Spyros Sioutas, Athanasios Tsakalidis, Kostas Tsichlas, and Christos Zaroliagis. Improved bounds for finger search
- Kaporis, Makris
(Show Context)
Citation Context ...r. Skip lists [10] and finger search trees [3], for example, support finger searches in O(log δ) time, where δ is the rank distance between the given pointer and the query. On the RAM, Kaporis et al. =-=[9]-=- describe a data structure with O(1) worst-case update time and O(log log δ) expected search time for a large class of input distributions, where δ is the distance between the query and some finger. F... |

1 |
Stølting Brodal, Christos Makris, Spyros Sioutas, Athanasios Tsakalidis, and Kostas Tsichlas. Optimal solutions for the temporal precedence problem
- Gerth
(Show Context)
Citation Context ...edence problem, a list is maintained under insertions. Given two pointers into the list, the data structure must decide which element was inserted first. An optimal solution is given by Brodal et al. =-=[2]-=- that allows the latter operation to be completed in O(log log δ) time, where δ is temporal distance between the two given elements. In two or more dimensions, one concentrates on finding the (approxi... |

1 | Geometric approximation algorithms. Online at http://valis.cs.uiuc.edu/ ~sariel/teach/notes/aprx - Har-Peled - 2009 |