I/O Efficient Dynamic Data Structures for Longest Prefix Queries

We present an efficient data structure for finding the longest prefix of a query string q in a dynamic database of strings. When the database strings are prefixes of IP-addresses then this is the IP-lookup problem. Our data structure is I/O efficient. It supports a query with a string q using \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O(\log_{B}(n)+\frac{|q|}{B})$\end{document} I/O operations, where B is the size of a disk block. It also supports an insertion and a deletion of a string q with the same number of I/Os. The data structure requires O(n/B) blocks, and the running time for each operation is O(BlogB(n)+|q|).