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I/O Efficient Dynamic Data Structures for Longest Prefix Queries

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Abstract

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 \(O(\log_{B}(n)+\frac{|q|}{B})\) 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(Blog B (n)+|q|).

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Notes

  1. Line rate is the data transmission speed of a communication line or network. This is about 40 Gbps and more today (2011).

  2. A segment contains a node if it contains all points in its subtree.

  3. Each bit in this memory has 3 possible states: 0, 1, and “don’t care” (this is the reason for the word ternary). To fit into a memory cell a prefix is padded with “don’t cares”. The memory is “content associative” since we give it a specific content and we get back the location of this content.

  4. This is only a conceptual mapping we do not store each interval in the node to which it is mapped.

  5. The root may also represent a prefix of all the keys: In such case we assume that there is an edge entering the root which corresponds to this prefix.

  6. Note that when all the strings in the trie share a prefix the string depth of the root is equal to the length of this prefix.

  7. The reason for this extra factor of B in the query time is because the search in each Patricia trie along the path could take O(B) time if the trie is highly unbalanced. The same happens with the string B-tree [10].

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Authors and Affiliations

  1. Faculty of Electrical Engineering, Tel Aviv University, Tel Aviv, 69978, Israel

    Moshe Hershcovitch

  2. School of Computer Science, Tel Aviv University, Tel Aviv, 69978, Israel

    Haim Kaplan

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  1. Moshe Hershcovitch
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  2. Haim Kaplan
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Correspondence to Haim Kaplan.

Additional information

This work is partially supported by United states—Israel Binational Science Foundation, project number 2006204.

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Hershcovitch, M., Kaplan, H. I/O Efficient Dynamic Data Structures for Longest Prefix Queries. Algorithmica 65, 371–390 (2013). https://doi.org/10.1007/s00453-011-9594-2

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