S(b)-Trees: An Optimal Balancing of Variable Length Keys

The paper studies the problem of maintaining external dynamic dictionaries with variable length keys. We introduce a new type of balanced trees, called S(b)-trees, which generalize traditional B-trees. Contrary to B-trees S(b)-trees provide optimal utilization of keys of variable length, while the data access time remains logarithmical, the same as for B-trees. The main property of the new trees is their local incompressibility. That is, any sequence consisting of b + 1 neighboring nodes of the tree cannot be compressed into a b well formed nodes. We prove 1 utilization lower bound for these trees where is inversely proportional to the tree branching. Logarithmic running time algorithms for search, insertion, and deletion are presented. The data structure is a flexible storage solution for semi-structured data and XML databases.

• Type: Conference
• Year: 2004
• Where: MSV
• Authors: Konstantin V. Shvachko
• Keywords: MSV 2004, MSV 2007, Traditional B-trees, Variable Length, Variable Length Keys