## Worst case constant time priority queue (2001)

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Venue: | In Proc. 12th ACM-SIAM Symposium on Discrete Algorithms |

Citations: | 11 - 4 self |

### BibTeX

@INPROCEEDINGS{Brodnik01worstcase,

author = {Andrej Brodnik and Svante Carlsson and Johan Karlsson and J. Ian Munro},

title = {Worst case constant time priority queue},

booktitle = {In Proc. 12th ACM-SIAM Symposium on Discrete Algorithms},

year = {2001},

pages = {523--528}

}

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### Abstract

We present a new data structure of size O(M) for solving the vEB problem. When this data structure is used in combination with a new memory topology it provides an O(1) worst case time solution. 1

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Citation Context ...hine model (cf. [10]) Mehlhorn et al. proved an amortized lower bound of Ω(lg lg M) [8]. Recently, Beame and Fich [2] gave a lower bound of Ω( � lg N/ lg lg N) under the communication game model (cf. =-=[9, 13]-=-) which also apply to the cell probe (cf. [14]) and RAM (cf. [11]) models. They also gave a matching upper bound for the static vEB problem. Andersson and Thorup [1] gave a data structure and an algor... |

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Citation Context ...es the space requirements from 2Mw+M+O(w)bitsto4M+O(w)bitsofconventional memory for the vEB problem. However, reducing the size increases the constant for the time. Or we can use perfect hashing (cf. =-=[6]-=-) to store the internal nodes that are tagged. This gives a space requirement of O(N) word instead of O(M/lg M) words of ordinary memory. The above discussion leads to the following Theorem: Theorem 1... |

200 |
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Citation Context ...re is used in combination with a new memory topology it provides an O(1) worst case time solution. 1 Introduction In this paper we will look at a problem, which was introduced by van Emde Boas et al. =-=[12]-=- as the extended repertoire of the Priority Queue problem, commonly called vEB. We present a solution to the vEB problem using a new data structure called Split Tagged Tree. Together with a new memory... |

139 | Should tables be sorted
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Citation Context ...mortized lower bound of Ω(lg lg M) [8]. Recently, Beame and Fich [2] gave a lower bound of Ω( � lg N/ lg lg N) under the communication game model (cf. [9, 13]) which also apply to the cell probe (cf. =-=[14]-=-) and RAM (cf. [11]) models. They also gave a matching upper bound for the static vEB problem. Andersson and Thorup [1] gave a data structure and an algorithm with a matching worst case time for the d... |

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Citation Context ...e solution for the vEB problem. The RAMBO model of computation is a RAM model in which, in one part of the memory, registers can share bits; i.e. bytes overlap (cf. RAMBO introduced by Fredman et al. =-=[7]-=- and further described by Brodnik [4]). One particular implementation of the RAMBO called Yggdrasil can help us to solve our problem.sIn the Yggdrasil memory implementation the registers overlap in th... |

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Log-logarithmic worst-case range queries are possible in space theta(n
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Citation Context ...does increase the, still constant, runtime. We can reduce the space even further by using perfect hashing to store tagged internal nodes in a manner similar to Willard's approach for stratified trees =-=[13]-=-. This gives a space requirement of O(NlgM) bits of ordinary memory and M bits of Yggdrasil memory. The above discussion leads to our main result: THEOREM 3.1. Using the Split-Tagged-Tree together wit... |

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Citation Context ... [7] for our problem. Recently, Beame and Fich [2] gave a lower bound of fi(~/lg N/lg lg N) under the communication game model (cf. [8, 14]) which also apply to the cell probe (cf. [15]) and RAM (cf. =-=[11]-=-) models. They also gave a matching upper bound for the static version of our problem. Andersson and Thorup [1] gave a data structure and an algorithm with a matching worst case time for the dynamic v... |

67 |
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Citation Context ...note lg M. Lower Bounds and some Matching Upper Bounds The obvious lower bound Ω(1) for the the vEB operations has been improved in various models of computation. Under the pointer machine model (cf. =-=[10]-=-) Mehlhorn et al. proved an amortized lower bound of Ω(lg lg M) [8]. Recently, Beame and Fich [2] gave a lower bound of Ω( � lg N/ lg lg N) under the communication game model (cf. [9, 13]) which also ... |

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Citation Context ...B operations has been improved in various models of computation. Under the pointer machine model (cf. [10]) Mehlhorn et al. proved an amortized lower bound of Ω(lg lg M) [8]. Recently, Beame and Fich =-=[2]-=- gave a lower bound of Ω( � lg N/ lg lg N) under the communication game model (cf. [9, 13]) which also apply to the cell probe (cf. [14]) and RAM (cf. [11]) models. They also gave a matching upper bou... |

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Citation Context ...hine model (cf. [10]) Mehlhorn et al. proved an amortized lower bound of Ω(lg lg M) [8]. Recently, Beame and Fich [2] gave a lower bound of Ω( � lg N/ lg lg N) under the communication game model (cf. =-=[9, 13]-=-) which also apply to the cell probe (cf. [14]) and RAM (cf. [11]) models. They also gave a matching upper bound for the static vEB problem. Andersson and Thorup [1] gave a data structure and an algor... |

40 | Tight(er) worst-case bounds on dynamic searching and priority queues
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(Show Context)
Citation Context ...tion game model (cf. [8,14]) which also apply to the cell probe (cf. [15]) and RAM (cf. [11]) models. They also gave a matching upper bound for the static version of our problem. Andersson and Thorup =-=[1]-=- gave a data structure and an algorithm with a matching worst case time for the dynamic version. Our Model of Computation Our model is based on the RAM model of computation which includes branching an... |

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Citation Context ...ower bound Ω(1) for the the vEB operations has been improved in various models of computation. Under the pointer machine model (cf. [10]) Mehlhorn et al. proved an amortized lower bound of Ω(lg lg M) =-=[8]-=-. Recently, Beame and Fich [2] gave a lower bound of Ω( � lg N/ lg lg N) under the communication game model (cf. [9, 13]) which also apply to the cell probe (cf. [14]) and RAM (cf. [11]) models. They ... |

17 |
Design and implementation of an ecient priority queue
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Citation Context ... combination with a new memory topology it provides an O(1) worst case time solution. 1 Introduction In this paper we reexamine the well known "discrete priority queue" problem of van Emde B=-=oas et al [12]-=-. Operating over the bounded universe of integers M = [0, .., M - 1], the usual operations of insert and extractmin are supported, as are the additional operations of extracting any value and findings... |

15 | Computation of the least significant set bit
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Citation Context ... it with extended RAM (ERAM). Operations to search for Least (Most) Significant Bit (LSB, MSB) can be implemented to run in O(1) time in the ERAM model, using a technique called Word-Size-Parallelism =-=[3]-=-. Hence, we let these operation be defined in the model as well.s2 Previous Related Work To solve the vEB problem, van Emde Boas et al. [12] introduced a data structure called Stratified Tree. Definit... |

10 |
M.: Tight(er) worst-case bounds on dynamic searching and priority queues
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(Show Context)
Citation Context ... communication game model (cf. [9, 13]) which also apply to the cell probe (cf. [14]) and RAM (cf. [11]) models. They also gave a matching upper bound for the static vEB problem. Andersson and Thorup =-=[1]-=- gave a data structure and an algorithm with a matching worst case time for the dynamic version. Our Model of Computation Our model is based on the RAM model of computation which includes branching an... |

10 | Searching in Constant Time and Minimum Space (Minimæ Res Magni Momenti Sunt
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Citation Context ...AMBO model of computation is a RAM model in which, in one part of the memory, registers can share bits; i.e. bytes overlap (cf. RAMBO introduced by Fredman et al. [7] and further described by Brodnik =-=[4]-=-). One particular implementation of the RAMBO called Yggdrasil can help us to solve our problem.sIn the Yggdrasil memory implementation the registers overlap in the form of a complete binary tree (Fig... |

4 |
Design of high performance memory module on PC100
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Citation Context ...andard heap order. The most significant bit m − 1of such a register is found in the root of the tree and in general: Bit j in register : 2 1 reg[i].bit[j] =Bk where k =(idiv2 j )+2 m−j−1 3 B 1 B 2 reg=-=[5]-=- 0 B8 B9 B10 B11 B12 B13 B14 B15 Register: 0 1 2 3 4 5 6 7 B 3 B 4 B 5 B 6 B 7 Figure 2: Overlapped memory Yggdrasil. (1) We now store the tags of the STT in the Yggdrasil memory, reg. The tree of int... |

2 |
Emde Boas. Machine Models and Simulations, volume A: Algorithms and Complexity
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Citation Context ...d of Ω(lg lg M) [8]. Recently, Beame and Fich [2] gave a lower bound of Ω( � lg N/ lg lg N) under the communication game model (cf. [9, 13]) which also apply to the cell probe (cf. [14]) and RAM (cf. =-=[11]-=-) models. They also gave a matching upper bound for the static vEB problem. Andersson and Thorup [1] gave a data structure and an algorithm with a matching worst case time for the dynamic version. Our... |

2 |
Storage modifications machines
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(Show Context)
Citation Context ... successor as its right neighbor. The neighbors of e are, then, its left and right neighbors, m will denote lg M. 1.1 Lower Bounds and some Matching Upper Bounds. Under the pointer machine model (cf. =-=[10]-=-) Mehlhorn et al. proved an amortized lower bound of f~(lglgM) [7] for our problem. Recently, Beame and Fich [2] gave a lower bound of fi(~/lg N/lg lg N) under the communication game model (cf. [8, 14... |

1 |
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Citation Context ...oving any value from the set and of finding the predecessor (largest element less than the given value) or successor (smallest greater) of a given value. The problem is referred to by Mehlhorn et al. =-=[7]-=- as the union-split-find problem. Under this terminology, one thinks of [0, .., M- 1] as being partitioned into subranges that can be further subdivided or merged, and that one can ask for the subrang... |

1 |
http : //www. pantheon, org/mythica/artieles/y/ yggdrasil, html
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Citation Context ...blem. (Yggdrasil according to Norse mythology is the great ash tree that holds together heaven, hell and earth with its roots and branches ... a task clearly requiring a nonstandard architecture, see =-=[9]-=-.) In the Yggdrasil memory layout, registers overlap as paths from root to leaf in a complete binary tree (see Figure 2). In particular, we think of the bits Bk(k=l,..,M-1) as being enumerated in stan... |