Competitive Online Search Trees on Trees

被引:0
|
作者
Bose, Prosenjit [1 ]
Cardinal, Jean [2 ]
Iacono, John [2 ]
Kountoutsos, Grigorios [2 ]
Langerman, Stefan [2 ]
机构
[1] Carleton Univ, Ottawa, ON, Canada
[2] Univ Libre Bruxelles ULB, Brussels, Belgium
来源
PROCEEDINGS OF THE 2020 ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, SODA | 2020年
关键词
DYNAMIC FINGER CONJECTURE; BINARY SEARCH; SPLAY TREES;
D O I
暂无
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
We consider the design of adaptive data structures for searching elements of a tree-structured space. We use a natural generalization of the rotation-based online binary search tree model in which the underlying search space is the set of vertices of a tree. This model is based on a simple structure for decomposing graphs, previously known under several names including elimination trees, vertex rankings, and tubings. The model is equivalent to the classical binary search tree model exactly when the underlying tree is a path. We describe an online O(log log n)-competitive search tree data structure in this model, matching the best known competitive ratio of binary search trees. Our method is inspired by Tango trees, an online binary search tree algorithm, but critically needs several new notions including one which we call Steiner-closed search trees, which may be of independent interest. Moreover our technique is based on a novel use of two levels of decomposition, first from search space to a set of Steiner-closed trees, and secondly from these trees into paths.
引用
收藏
页码:1878 / 1891
页数:14
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