Time series play a crucial role in many fields, including finance, healthcare, industry, and environmental monitoring. The storage and retrieval of time series can be challenging due to their unstoppable growth. In fact, these applications often sacrifice precious historical data to make room for new data. General-purpose compressors like Xz and Zstd can mitigate this problem with their good compression ratios, but they lack efficient random access on compressed data, thus preventing real-time analyses. Ad-hoc streaming solutions, instead, typically optimise only for compression and decompression speed, while giving up compression effectiveness and random access functionality. Furthermore, all these methods lack awareness of certain special regularities of time series, whose trends over time can often be described by some linear and nonlinear functions. To address these issues, we introduce NeaTS, a randomly-accessible compression scheme that approximates the time series with a sequence of nonlinear functions of different kinds and shapes, carefully selected and placed by a partitioning algorithm to minimise the space. The approximation residuals are bounded, which allows storing them in little space and thus recovering the original data losslessly, or simply discarding them to obtain a lossy time series representation with maximum error guarantees. Our experiments show that NeaTS improves the compression ratio of the state-of-the-art lossy compressors that use linear or nonlinear functions (or both) by up to 14%. Compared to lossless compressors, NeaTS emerges as the only approach to date providing, simultaneously, compression ratios close to or better than the best existing compressors, a much faster decompression speed, and orders of magnitude more efficient random access, thus enabling the storage and real-time analysis of massive and ever-growing amounts of (historical) time series data.

We study the problem of engineering space-time efficient data structures that support membership and rank queries on very large static dictionaries of strings. Our solution is based on a very simple approach that decouples string storage and string indexing by means of a block-wise compression of the sorted dictionary strings (to be stored in external memory) and a succinct implementation of a Patricia trie (to be stored in internal memory) built on the first string of each block. On top of this, we design an in-memory cache that, given a sample of the query workload, augments the Patricia trie with additional information to reduce the number of I/Os of future queries. Our experimental evaluation on two new datasets, which are at least one order of magnitude larger than the ones used in the literature, shows that (i) the state-of-the-art compressed string dictionaries, compared to Patricia tries, do not provide significant benefits when used in a large-scale indexing setting, and (ii) our two-level approach enables the indexing and storage of 3.5 billion strings taking 273 GB in just less than 200 MB of internal memory and 83 GB of compressed disk space, while still guaranteeing comparable or faster query performance than those offered by array-based solutions used in modern storage systems, such as RocksDB, thus possibly influencing their future design.

We address the problem of compressing and indexing a sorted dictionary of strings to support efficient lookups and more sophisticated operations, such as prefix, predecessor, and range searches. This problem occurs as a key task in a plethora of applications, and thus it has been deeply investigated in the literature since the introduction of tries in the ’60s. We introduce a new data structure, called the COmpressed COllapsed Trie (CoCo-trie), that hinges on a pool of techniques to compress subtries (of arbitrary depth) into succinctly-encoded and efficiently-searchable trie macro-nodes with a possibly large fan-out. Then, we observe that the choice of the subtries to compress depends on the trie structure and its edge labels. Hence, we develop a data-aware optimisation approach that selects the best subtries to compress via the above pool of succinct encodings, with the overall goal of minimising the total space occupancy and still achieving efficient query time. We also investigate some variants of this approach that induce interesting space–time trade-offs in the CoCo-trie design. Our experimental evaluation on six diverse and large datasets (representing URLs, XML data, DNA and protein sequences, database records, and search-engine dictionaries) shows that the space–time performance of well-established and highly-engineered data structures solving this problem is very input-sensitive. Conversely, our CoCo-trie provides a robust and uniform improvement over all competitors for half of the datasets, and it results on the Pareto space–time frontier for the others, thus offering new competitive trade-offs.

Range filters allow checking whether a query range intersects a given set of keys with a chance of returning a false positive answer, thus generalising the functionality of Bloom filters from point to range queries. Existing practical range filters have addressed this problem heuristically, resulting in high false positive rates and query times when dealing with adversarial inputs, such as in the common scenario where queries are correlated with the keys. We introduce Grafite, a novel range filter that solves these issues with a simple design and clear theoretical guarantees that hold regardless of the input data and query distribution: given a fixed space budget of B bits per key, the query time is O(1), and the false positive probability is upper bounded by l/2B-2, where l is the query range size. Our experimental evaluation shows that Grafite is the only range filter to date to achieve robust and predictable false positive rates across all combinations of datasets, query workloads, and range sizes, while providing faster queries and construction times, and dominating all competitors in the case of correlated queries. As a further contribution, we introduce a very simple heuristic range filter whose performance on uncorrelated queries is very close to or better than the one achieved by the best heuristic range filters proposed in the literature so far.

We present the first learned index that supports predecessor, range queries and updates within provably efficient time and space bounds in the worst case. In the (static) context of just predecessor and range queries these bounds turn out to be optimal. We call this learned index the Piecewise Geometric Model index (PGM-index). Its flexible design allows us to introduce three variants which are novel in the context of learned data structures. The first variant of the PGM-index is able to adapt itself to the distribution of the query operations, thus resulting in the first known distribution-aware learned index to date. The second variant exploits the repetitiveness possibly present at the level of the learned models that compose the PGM-index to further compress its succinct space footprint. The third one is a multicriteria variant of the PGM-index that efficiently auto-tunes itself in a few seconds over hundreds of millions of keys to satisfy space-time constraints which evolve over time across users, devices and applications. These theoretical achievements are supported by a large set of experimental results on known datasets which show that the fully-dynamic PGM-index improves the space occupancy of existing traditional and learned indexes by up to three orders of magnitude, while still achieving their same or even better query and update time efficiency. As an example, in the static setting of predecessor and range queries, the PGM-index matches the query performance of a cache-optimised static B+-tree within two orders of magnitude (83×) less space; whereas in the fully-dynamic setting, where insertions and deletions are allowed, the PGM-index improves the query and update time performance of a B + -tree by up to 71% within three orders of magnitude (1140×) less space.