## Improving Partial Rebuilding by Using Simple Balance Criteria

Citations: | 21 - 4 self |

### BibTeX

@MISC{Andersson_improvingpartial,

author = {Arne Andersson},

title = {Improving Partial Rebuilding by Using Simple Balance Criteria},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

Some new classes of balanced trees, defined by very simple balance criteria, are introduced. Those trees can be maintained by partial rebuilding at lower update cost than previously used weight-balanced trees. The used balance criteria also allow us to maintain a balanced tree without any balance information stored in the nodes.

### Citations

1115 |
Multidimensional binary search trees used for associative searching
- Bentley
- 1975
(Show Context)
Citation Context ...f a subtree takes linear time, Rjvj where v is the root of the subtree. Partial rebuilding is also applyable in cases when a rebuilding at v takes longer time, for example when maintaining quad trees =-=[4]-=-. The improvements we make are also valid in those cases. 1.1 Weight-Balancing The idea of weight-balancing is to control the height of a tree by limiting the quotient between the sizes of the two sub... |

371 |
Self-adjusting binary search trees
- Sleator, Tarjan
- 1985
(Show Context)
Citation Context ... is to allow the tree to take any shape as long as its height is O(log n). Such a balance criterion results in a "superclass" containing all other classes of balanced trees. (Note that the s=-=play tree [11]-=- is not balanced in this sense, since its worst case height is O(n).) In this section we show that such a superclass may be maintained by partial rebuilding. This class also has the advantage of requi... |

113 |
Symmetric Binary B-trees: Data structures and maintenance algorithms
- Bayer
- 1972
(Show Context)
Citation Context ... simplicity of the balance criterion makes trees of bounded height a natural class which contains most other classes of balanced trees. This is the case for AVL-trees [1], BB(ff)-trees [7], SBB-trees =-=[3]-=-, and ffBB-trees [8]. For all those classes there exist a constant u such that height(v)su log jvj + 1 for each node v in the tree. 3 General Balanced Trees Allthough the BH(u)-trees are a general cla... |

30 |
Dynamic multi-dimensional data structures based on quad- and k-d trees
- Overmars, Leeuwen
- 1982
(Show Context)
Citation Context ... a balanced tree without any balance information stored in the nodes. 1 Introduction Partial rebuilding is a general method to maintain balanced tree structures introduced by Overmars and van Leeuwen =-=[9, 10]-=-. The idea is brutal but powerful; each time a given balance criterion is violated at a node v we rebuild the subtree rooted at v to perfect balance. The simplicity of this method makes it useful in a... |

29 |
An algorithm for the organization of information. Doklady Akademii Nauk SSSR, 146:263–266, (Russian). English translation by Myron
- Adelson-Velskii, Landis
- 1962
(Show Context)
Citation Context ...tized cost actually is lower. The simplicity of the balance criterion makes trees of bounded height a natural class which contains most other classes of balanced trees. This is the case for AVL-trees =-=[1]-=-, BB(ff)-trees [7], SBB-trees [3], and ffBB-trees [8]. For all those classes there exist a constant u such that height(v)su log jvj + 1 for each node v in the tree. 3 General Balanced Trees Allthough ... |

27 |
The design of dynamic data structures, volume 156
- Overmars
(Show Context)
Citation Context ... a balanced tree without any balance information stored in the nodes. 1 Introduction Partial rebuilding is a general method to maintain balanced tree structures introduced by Overmars and van Leeuwen =-=[9, 10]-=-. The idea is brutal but powerful; each time a given balance criterion is violated at a node v we rebuild the subtree rooted at v to perfect balance. The simplicity of this method makes it useful in a... |

16 |
A new class of balanced search trees; half-balanced binary search trees
- Olivie
(Show Context)
Citation Context ...alance criterion makes trees of bounded height a natural class which contains most other classes of balanced trees. This is the case for AVL-trees [1], BB(ff)-trees [7], SBB-trees [3], and ffBB-trees =-=[8]-=-. For all those classes there exist a constant u such that height(v)su log jvj + 1 for each node v in the tree. 3 General Balanced Trees Allthough the BH(u)-trees are a general class of trees this cla... |

13 |
A comparison of tree-balancing algorithms
- Baer, Schwab
- 1977
(Show Context)
Citation Context ... the algorithms for BB(ff)-trees and BH(u)-trees. Since there is no local balance criterion to be fulfilled in each node the balance criterion is checked only at the root. As shown by Baer and Schwab =-=[2]-=-, if we rebalance the entire tree each time it becomes too high the amortized cost will be O(n) per updating operation. To achieve a better result we make the following observation: Lemma 4 Let T be a... |

10 |
Binary trees of bounded balance
- Nievergelt, Reingold
- 1973
(Show Context)
Citation Context ...ing the quotient between the sizes of the two subtrees of each node. Trees maintained in this way is called trees of bounded balance or BB(ff)-trees and was first presented by Nievergelt and Reingold =-=[7]-=-. The maintenance of BB(ff)-trees by partial rebuilding is briefly analyzed in [9] We give a short analysis here. An alternative definition is also given (equation (3) below). Associated with the tree... |

9 |
Implementing dictionaries using binary trees of very small height. Information Processing Letters
- Mauer, Ottmann, et al.
- 1976
(Show Context)
Citation Context ... + 1 for each node v in the tree. 3 General Balanced Trees Allthough the BH(u)-trees are a general class of trees this class does not contain all balanced trees, for example not the k-neighbour trees =-=[6]. The simp-=-liest possible balance criterion we can have is to allow the tree to take any shape as long as its height is O(log n). Such a balance criterion results in a "superclass" containing all other... |

5 |
Addendum to "A Storage Scheme for Height-Balanced Trees
- Brown
- 1979
(Show Context)
Citation Context ...lanced in the sense that the height is guaranteed to be O(log n). The logarithmic cost for searching in a splay tree is amortized while we here obtain logarithmic worst case bounds. As shown by Brown =-=[5]-=- the explicit balance information may in some classes of balanced trees be eliminated by coding the information by the location of empty pointers. However, in this case we still store the information ... |