## Skip trees, an alternative data structure to Skip lists in a concurrent approach (1997)

Citations: | 2 - 0 self |

### BibTeX

@MISC{Messeguer97skiptrees,,

author = {Xavier Messeguer},

title = {Skip trees, an alternative data structure to Skip lists in a concurrent approach},

year = {1997}

}

### OpenURL

### Abstract

We present a new type of search trees, called Skip trees, which are a generalization of Skip lists. To be precise, there is a one-to-one mapping between the two data types which commutes with the sequential update algorithms. A Skip list is a data structure used to manage data bases which stores values in a sorted way and in which it is insured that the form of the Skip list is independent of the order of updates by using randomization techniques. Skip trees inherit all the properties of Skip lists, including the time bounds of sequential algorithms. The algorithmic improvement of the Skip tree type is that a concurrent algorithm on the fly approach can be designed. Among other advantages, this algorithm is more compressive than the one designed by Pugh for Skip lists and accepts a higher degree of concurrence because it is based on a set of local updates. From a practical point of view, although the Skip list should be in the main memory, Skip trees can be registered into a secondary...

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Citation Context ... indexer des bases de donn'ees en comparison avec les B-trees. 1 Introduction This paper follows on from the attempt to design a concurrent algorithm on the fly approach for Skip lists. The Skip list =-=[22]-=- is a data structure that stores values in a sorted order (see Figure 1). It plays an important role because, by means of randomization, the form of the Skip list is independent of the order of update... |

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Citation Context ...sts a one-to-one mapping that commutes with updates between AVL trees and 1--2 Brother trees. Finally, Skip trees have the same performance rates as the random search trees by R. Seidel and C. Aragon =-=[23]-=-. However, random search trees should be applied in a different context, because the probability of a key is given by a continuous identically distributed random variable. This paper has six sections.... |

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Citation Context ...0]: once new keys have been inserted, the tree is balanced with a set of local evolution rules. This approach was further applied in [1, 13, 14, 15]. The concurrent algorithm on Skip lists by W. Pugh =-=[21]-=- is far from being composed of local rules and needs some kind of circular pointers to maintain information. These two facts cast doubts as to the comprehensiveness and correctness of the algorithm. W... |

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Citation Context ...t to apply this approach to search trees, specifically AVL trees [10]: once new keys have been inserted, the tree is balanced with a set of local evolution rules. This approach was further applied in =-=[1, 13, 14, 15]-=-. The concurrent algorithm on Skip lists by W. Pugh [21] is far from being composed of local rules and needs some kind of circular pointers to maintain information. These two facts cast doubts as to t... |

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Citation Context ...xpected efficiency of updates is comparable with other equilibrated structures such as AVL trees and B-trees. In the last five years there have been a great number of reports analysing its properties =-=[3, 11, 18, 24]-=-. The concurrent on the fly approach, which allows a very high degree of concurrence, is inspired by [5]. This paper proposes a Garbage collection concurrent algorithm consisting of the main algorithm... |

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Citation Context ...xpected efficiency of updates is comparable with other equilibrated structures such as AVL trees and B-trees. In the last five years there have been a great number of reports analysing its properties =-=[3, 11, 18, 24]-=-. The concurrent on the fly approach, which allows a very high degree of concurrence, is inspired by [5]. This paper proposes a Garbage collection concurrent algorithm consisting of the main algorithm... |

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Citation Context ...xpected efficiency of updates is comparable with other equilibrated structures such as AVL trees and B-trees. In the last five years there have been a great number of reports analysing its properties =-=[3, 11, 18, 24]-=-. The concurrent on the fly approach, which allows a very high degree of concurrence, is inspired by [5]. This paper proposes a Garbage collection concurrent algorithm consisting of the main algorithm... |

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Citation Context ... has the same performance as the sequential updates time of Skip lists. Given a Skip tree T , the inverse S = T \Gamma1 (T ) is a Skip list. Therefore we transferre the results obtained in Skip lists =-=[22, 7]-=-: Theorem 2 Let T be a Skip tree of size n and random parameter q. The expected time for searching, inserting or deleting a key is O(log 1=p n) and the probability that the expected height deviates k ... |

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Citation Context ...t to apply this approach to search trees, specifically AVL trees [10]: once new keys have been inserted, the tree is balanced with a set of local evolution rules. This approach was further applied in =-=[1, 13, 14, 15]-=-. The concurrent algorithm on Skip lists by W. Pugh [21] is far from being composed of local rules and needs some kind of circular pointers to maintain information. These two facts cast doubts as to t... |

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Citation Context ...to nodes of trees, therefore the design of algorithms can be based on sets of local rules. Moreover, as there is a one-to-one mapping between 1 This idea was applied by T. Papadakis in his PhD thesis =-=[17]-=- to introduce deterministic Skip list. 2 20 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. .. ........ |

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Citation Context ... last five years there have been a great number of reports analysing its properties [3, 11, 18, 24]. The concurrent on the fly approach, which allows a very high degree of concurrence, is inspired by =-=[5]-=-. This paper proposes a Garbage collection concurrent algorithm consisting of the main algorithm, which dynamically puts nodes onto the structure and takes them away, and the garbage collector, which ... |

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Citation Context ...e finally introduce the rule attach(S; a) and unattach(S; a) that attaches and unattaches key a to nodes with level 1. 2 Some authors count the number of trials instead of the number of failures (see =-=[20]-=-). 5 3 Skip trees A Skip tree is a search tree. Each internal node n has three registers: height(n) gives us the height of the node, key(n) stores a possibly empty ordered list of keys and child(n) st... |

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Citation Context ...t to apply this approach to search trees, specifically AVL trees [10]: once new keys have been inserted, the tree is balanced with a set of local evolution rules. This approach was further applied in =-=[1, 13, 14, 15]-=-. The concurrent algorithm on Skip lists by W. Pugh [21] is far from being composed of local rules and needs some kind of circular pointers to maintain information. These two facts cast doubts as to t... |

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Citation Context ...s and R. Sedgewick [8] embed schemes in a dichromatic frame. T. Papadakis [17] gives us a one-to-one mapping between 2--3 trees and deterministic Skip lists. Later on T. Ottmann, H. Six and D. 3 Wood =-=[16]-=- prove that there exists a one-to-one mapping that commutes with updates between AVL trees and 1--2 Brother trees. Finally, Skip trees have the same performance rates as the random search trees by R. ... |

4 |
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Citation Context ...the design of massively parallel algorithms for Skip trees. The state of the art is that W. Paul, U. Vishkin and H. Wagener [19] designed a parallel algorithm for 2--3 trees, L. Higham and E. Schenks =-=[9]-=- designed one for B-trees, and J. Gabarr'o, C. Mart'inez and X. Messeguer [7] designed a parallel algorithm for Skip lists. Thus, the parallel algorithm of Skip trees will arise from the right mixture... |

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1 |
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(Show Context)
Citation Context ...hange pages many times. Skip trees, thanks to their structure, allow more efficient pagination. Moreover, due to their relationships with B-trees, the improvements proposed by G. Diehr and B. Faaland =-=[4]-=- can be applied. Recall that mappings between data structures are a well-known topic. L. Guibas and R. Sedgewick [8] embed schemes in a dichromatic frame. T. Papadakis [17] gives us a one-to-one mappi... |

1 |
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(Show Context)
Citation Context ...race properties from Skip lists, and structural and algorithmic improvements from the family of B-trees. For instance, an example of a structural improvement is the defintion, by following C. Douglas =-=[6]-=-, of Skip trees or Skip + trees. And an example of algorithmic improvements is that we can translate algorithms from B-trees to Skip trees by taking parameter q ' 1, or from 2--3 trees to Skip trees b... |

1 |
Pagination of B trees with variable length records
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(Show Context)
Citation Context ...r the length of nodes: for instance, c = 1 determines that about n=e nodes grows more than the expected value. This fact suggests implementing Skip trees with nodes of variable length as E. McCreight =-=[12]-=- or G. Diehr and B. Faaland [4] propose for B-trees. 6 Conclusions and further research From a theoretical point of view, the balanced search trees can be separated into two groups depending on the se... |