Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1103.0248

DB Category: Denotational Semantics for View-based Database Mappings

Zoran Majkic
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present a categorical denotational semantics for a database mapping, based on views, in the most general framework of a database integration/exchange. Developed database category DB, for databases (objects) and view-based mappings (morphisms) between them, is different from Set category: the morphisms (based on a set of complex query computations) are not functions, while the objects are database instances (sets of relations). The logic based schema mappings between databases, usually written in a highly expressive logical language (ex. LAV, GAV, GLAV mappings, or tuple generating dependency) may be functorially translated into this "computation" category DB. A new approach is adopted, based on the behavioral point of view for databases, and behavioral equivalences for databases and their mappings are established. By introduction of view-based observations for databases, which are computations without side-effects, we define a fundamental (Universal algebra) monad with a power-view endofunctor T. The resulting 2-category DB is symmetric, so that any mapping can be represented as an object (database instance) as well, where a higher-level mapping between mappings is a 2-cell morphism. Database category DB has the following properties: it is equal to its dual, complete and cocomplete. Special attention is devoted to practical examples: a query definition, a query rewriting in GAV Database-integration environment, and the fixpoint solution of a canonical data integration model.

Explore related subjects

cs.DBcs.LOmath.CT

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Zoran Majkic. 2011-02-24. DB Category: Denotational Semantics for View-based Database Mappings. https://arxiv.org/abs/1103.0248

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

VectorMaton: Efficient Vector Search with Pattern Constraints via an Enhanced Suffix Automaton

Approximate nearest neighbor search (ANNS) has become a cornerstone in modern vector database systems. Given a query vector, ANNS retrieves the closest vectors from a set of base vectors. In real-world applications, vectors are often accompanied by additional information, such as sequences or structured attributes, motivating the need for fine-grained vector search with constraints on this auxiliary data. Existing methods support attribute-based filtering or range-based filtering on categorical and numerical attributes, but they do not support pattern predicates over sequence attributes. In relational databases, predicates such as LIKE and CONTAINS are fundamental operators for filtering records based on substring patterns. As vector databases increasingly adopt SQL-style query interfaces, enabling pattern predicates over sequence attributes (e.g., texts and biological sequences) alongside vector similarity search becomes essential. In this paper, we formulate a novel problem: given a set of vectors each associated with a sequence, retrieve the nearest vectors whose sequences contain a given query pattern. To address this challenge, we propose VectorMaton, an automaton-based index that integrates pattern filtering with efficient vector search, while maintaining an index size comparable to the dataset size. Extensive experiments on real-world datasets demonstrate that VectorMaton consistently outperforms all baselines, achieving up to 10x higher query throughput at the same accuracy and up to 18x reduction in index size.

cs.DB↗
arXiv2026

Efficient K-generalizable Learned Search

Learned top-K search improves the accuracy-latency trade-off of graph-based vector search, but existing methods are designed for a fixed K: serving production workloads with varying K values requires preprocessing cost proportional to the number of distinct Ks served - prohibitive in practice. This paper shows that learned search can support arbitrary K with the preprocessing cost of a single top-1 model. The key idea is to reduce top-K learned search to repeated masked top-1 refinement, which works because the distance-reduction trajectory for discovering the next top-1 vector is largely invariant to the number of results already found. We therefore train the model on trajectory features that remain effective under masking. To make repeated refinement robust and efficient, OMEGA counters error accumulation across iterations with rank-wise confidence allocation, and skips unnecessary model invocations with a statistical forecast of recall from partial results. Across nine dataset-scale configurations, OMEGA meets the 0.95 recall target with one K-independent model. Under the lowest-preprocessing configuration of each learned baseline,it reduces mean latency by 7-36% versus DARTH, 3-25% versus MultiK-DARTH, and 8-21% versus LAET on BIGANN, BIGANN-1B, DEEP, and three production workloads. On GIST, Text2Image, and MS MARCO, its latency remains within 9% of DARTH and MultiK-DARTH. On production traces, OMEGA further reduces total serving and preprocessing computation by up to 28%.

cs.DB↗
arXiv2026

Samyama: A Unified Graph-Vector Database with In-Database Optimization, Agentic Enrichment, and Hardware Acceleration

Modern data architectures fragment across graph databases, vector stores, analytics engines and optimization solvers, forcing ETL between them. We present Samyama, a graph-vector database in Rust that unifies these workloads in one engine: a RocksDB-backed store with MVCC, a vectorized executor, a cost-based planner, a CSR analytics engine, RDF and SPARQL, 22 metaheuristic solvers callable from the query language, HNSW vector indexing, and agentic enrichment that expands a graph via LLMs. It has been run to billion-edge scale: 74.3M nodes and 1.07B edges from four biomedical sources on one machine for $2.50 of spot compute. This version re-measures the system at release v1.8.0 on rented Linux hosts a reader can boot, replacing earlier figures taken on a Mac Mini that nobody could re-run. On a 16-vCPU cloud instance, ingestion reaches 123K-152K nodes/s and PageRank costs 6.7 ms per iteration at ten thousand nodes and 236 ms at a million. The previously reported 8.2x GPU speedup is withdrawn; in its place we measure the CUDA path, which no earlier version measured at all, on a rented NVIDIA A16: parity with the CPU at ten thousand nodes, 1.62x at a hundred thousand and 2.70x at a million, with 1.1-1.35 s of context initialisation on the first call. The earlier Cypher-throughput figure, its claim of near-constant index-driven scaling, and a vector-search figure are withdrawn as unreproducible. openCypher conformance, once estimated at ~90%, is now measured at 99.9% of evaluated TCK scenarios. Against Neo4j 5 and FalkorDB on one host over an identical SF10 extract, 14 of 14 SNB complex reads land within 5x of the best competitor and 7 of 14 are faster.

cs.DB↗