An order searching algorithm of extensible hashing

Abstract

Extensible hashing schemes provide fast key retrieval for dynamic key sets, but they can not keep order preserved searching. In order to solve this problem, Jonge et al. proposed the binary digital search tree (BDS-tree) that enables order preserved searching by extensible hashing schemes, and the method to change the BDS-tree into a compact bit stream (called the pre-order bit stream) However, searching and updating a key takes a lot of time in large key sets. This paper proposes a new method to preserve the key-order access property and to improve the time cost. The algorithms for retrieval, insertion and deletion of keys using this new method are introduced through examples. This method separates the BDS-tree into smaller trees of a certain depth, and creates the pre-order bit stream for each of the separated trees. The theoretical and experimental results, using 50,000 Japanese nouns, show that the presented method provides faster access than the traditional BDS-tree. Retrieval is 18 times, the insertion is 13 times and the deletion is 4 times faster. There is a small increase in the storage requirement for the separated BDS-tree. However, by nature, the pre-order bit stream is very compact in size, thus making the increase insignificant.