Top Tree Compression of Tries

Philip Bille; Inge Li Gørtz; Paweł Gawrychowski; Gad M. Landau; Oren Weimann

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arXiv · 1902.02187

Top Tree Compression of Tries

Philip Bille·Inge Li Gørtz·Paweł Gawrychowski·Gad M. Landau·Oren Weimann

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Abstract

We present a compressed representation of tries based on top tree compression [ICALP 2013] that works on a standard, comparison-based, pointer machine model of computation and supports efficient prefix search queries. Namely, we show how to preprocess a set of strings of total length $n$ over an alphabet of size $\sigma$ into a compressed data structure of worst-case optimal size $O(n/\log_\sigma n)$ that given a pattern string $P$ of length $m$ determines if $P$ is a prefix of one of the strings in time $O(\min(m\log \sigma,m + \log n))$. We show that this query time is in fact optimal regardless of the size of the data structure. Existing solutions either use $\Omega(n)$ space or rely on word RAM techniques, such as tabulation, hashing, address arithmetic, or word-level parallelism, and hence do not work on a pointer machine. Our result is the first solution on a pointer machine that achieves worst-case $o(n)$ space. Along the way, we develop several interesting data structures that work on a pointer machine and are of independent interest. These include an optimal data structures for random access to a grammar-compressed string and an optimal data structure for a variant of the level ancestor problem.

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BibTeX RIS

Philip Bille, Inge Li Gørtz, Paweł Gawrychowski, Gad M. Landau, Oren Weimann. 2019-02-06. Top Tree Compression of Tries. https://arxiv.org/abs/1902.02187

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