String Indexing with Compressed Patterns

Given a string S of length n, the classic string indexing problem is to preprocess S into a compact data structure that supports efficient subsequent pattern queries. In this paper we consider the basic variant where the pattern is given in compressed form and the goal is to achieve query time that is fast in terms of the compressed size of the pattern. This captures the common client-server scenario, where a client submits a query and communicates it in compressed form to a server. Instead of the server decompressing the query before processing it, we consider how to efficiently process the compressed query directly. Our main result is a novel linear space data structure that achieves near-optimal query time for patterns compressed with the classic Lempel-Ziv 1977 (LZ77) compression scheme. Along the way we develop several data structural techniques of independent interest, including a novel data structure that compactly encodes all LZ77 compressed suffixes of a string in linear space and a general decomposition of tries that reduces the search time from logarithmic in the size of the trie to logarithmic in the length of the pattern

Entropy-scaling search of massive biological data

Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing a dataset's entropy and fractal dimension. We prove that searching scales in time with metric entropy (number of covering hyperspheres), if the fractal dimension of the dataset is low, and scales in space with the sum of metric entropy and information-theoretic entropy (randomness of the data). Using these ideas, we present accelerated versions of standard tools, with no loss in specificity and little loss in sensitivity, for use in three domains---high-throughput drug screening (Ammolite, 150x speedup), metagenomics (MICA, 3.5x speedup of DIAMOND [3,700x BLASTX]), and protein structure search (esFragBag, 10x speedup of FragBag). Our framework can be used to achieve "compressive omics," and the general theory can be readily applied to data science problems outside of biology.Comment: Including supplement: 41 pages, 6 figures, 4 tables, 1 bo

Faster Compact On-Line Lempel-Ziv Factorization

We present a new on-line algorithm for computing the Lempel-Ziv factorization of a string that runs in $O(N\log N)$ time and uses only $O(N\log\sigma)$ bits of working space, where $N$ is the length of the string and $\sigma$ is the size of the alphabet. This is a notable improvement compared to the performance of previous on-line algorithms using the same order of working space but running in either $O(N\log^3N)$ time (Okanohara & Sadakane 2009) or $O(N\log^2N)$ time (Starikovskaya 2012). The key to our new algorithm is in the utilization of an elegant but less popular index structure called Directed Acyclic Word Graphs, or DAWGs (Blumer et al. 1985). We also present an opportunistic variant of our algorithm, which, given the run length encoding of size $m$ of a string of length $N$, computes the Lempel-Ziv factorization on-line, in $O\left(m \cdot \min \left\{\frac{(\log\log m)(\log \log N)}{\log\log\log N}, \sqrt{\frac{\log m}{\log \log m}} \right\}\right)$ time and $O(m\log N)$ bits of space, which is faster and more space efficient when the string is run-length compressible

Estimating Cardinalities with Deep Sketches

We introduce Deep Sketches, which are compact models of databases that allow us to estimate the result sizes of SQL queries. Deep Sketches are powered by a new deep learning approach to cardinality estimation that can capture correlations between columns, even across tables. Our demonstration allows users to define such sketches on the TPC-H and IMDb datasets, monitor the training process, and run ad-hoc queries against trained sketches. We also estimate query cardinalities with HyPer and PostgreSQL to visualize the gains over traditional cardinality estimators.Comment: To appear in SIGMOD'1

R3D3: A doubly opportunistic data structure for compressing and indexing massive data

Opportunistic data structures are used extensively in big data practice to break down the massive storage space requirements of processing large volumes of information. A data structure is called (singly) opportunistic if it takes advantage of the redundancy in the input in order to store it in informationtheoretically minimum space. Yet, efficient data processing requires a separate index alongside the data, whose size often substantially exceeds that of the compressed information. In this paper, we introduce doubly opportunistic data structures to not only attain best possible compression on the input data but also on the index. We present R3D3 that encodes a bitvector of length n and Shannon entropy H0 to nH0 bits and the accompanying index to nH0(1/2 + O(log C/C)) bits, thus attaining provably minimum space (up to small error terms) on both the data and the index, and supports a rich set of queries to arbitrary position in the compressed bitvector in O(C) time when C = o(log n). Our R3D3 prototype attains several times space reduction beyond known compression techniques on a wide range of synthetic and real data sets, while it supports operations on the compressed data at comparable speed