Join (sigma algebra)

About: Join (sigma algebra) is a research topic. Over the lifetime, 2510 publications have been published within this topic receiving 26401 citations. The topic is also known as: refinement.

Applications of Hyperstructure Theory

Abstract: Introduction. Basic notions and results on Hyperstructure Theory. 1: Some topics of Geometry. 1. Descriptive geometries and join spaces. 2. Spherical geometries and join spaces. 3. Projective geometries and join spaces. 4. Multivalued loops and projective geometries. 2: Graphs and Hypergraphs. 1. Generalized graphs and hypergroups. 2. Chromatic quasi-canonical hypergroups. 3. Hypergroups induced by paths of a direct graph. 4. Hypergraphs and hypergroups. 5. On the hypergroup HGamma associated with a hypergraph Gamma. 6. Other hyperstructures associated with hypergraphs. 3: Binary Relations. 1. Quasi-order hypergroups. 2. Hypergroups associated with binary relations. 3. Hypergroups associated with union, intersection, direct product, direct limit of relations. 4. Relation beta in semihypergroups. 4: Lattices. 1. Distributive lattices and join spaces. 2. Lattice ordered join space. 3. Modular lattices and join spaces. 4. Direct limit and inverse limit of join spaces associated with lattices. 5. Hyperlattices and join spaces. 5: Fuzzy sets and rough sets. 2. Direct limit and inverse limit of join spaces associated with fuzzy subsets. 3. Rough sets, fuzzy subsets and join spaces. 4. Direct limits and inverse limits of join spaces associated with rough sets. 5. Hyperstructures and Factor Spaces. 6. Hypergroups induced by a fuzzy subset. Fuzzy hypergroups. 7. Fuzzy subhypermodules over fuzzy hyperrings. 8. On Chinese hyperstructures. 6: Automata. 1. Language theory and hyperstructures. 2. Automata and hyperstructures. 3. Automata and quasi-order hypergroups. 7: Cryptography. 1. Algebraic cryptography and hypergroupoids. 2. Cryptographic interpretation of some hyperstructures. 8: Codes. 1. Steiner hypergroupoids and Steiner systems. 2. Some basic notions about codes. 3. Steiner hypergroups and codes. 9: Median algebras, Relation algebras, C-algebras. 1. Median algebras and join spaces. 2. Relation algebras and quasi-canonical hypergroups. 3. C-algebras and quasi-canonical hypergroups. 10: Artificial Intelligence. 1. Generalized intervals. Connections with quasi-canonical hypergroups. 2. Weak representations of interval algebras. 11: Probabilities. Bibliography.

Estimating the transition between two intersecting straight lines

Abstract: SUMMARY For experimental data which appear to behave according to two different distinct linear relationships, a general model is proposed which allows for a smooth transition from one linear regime to the other. The transition is accomplished by a curve incorporating a transition parameter. The special case of two intersecting straight lines is included in this model. A Bayesian estimation procedure is used to determine the plausibility of different parameter values. The analysis procedure may be extended to any number of join points and for any linear intersecting functions.

Join synopses for approximate query answering

Abstract: In large data warehousing environments, it is often advantageous to provide fast, approximate answers to complex aggregate queries based on statistical summaries of the full data. In this paper, we demonstrate the difficulty of providing good approximate answers for join-queries using only statistics (in particular, samples) from the base relations. We propose join synopses as an effective solution for this problem and show how precomputing just one join synopsis for each relation suffices to significantly improve the quality of approximate answers for arbitrary queries with foreign key joins. We present optimal strategies for allocating the available space among the various join synopses when the query work load is known and identify heuristics for the common case when the work load is not known. We also present efficient algorithms for incrementally maintaining join synopses in the presence of updates to the base relations. Our extensive set of experiments on the TPC-D benchmark database show the effectiveness of join synopses and various other techniques proposed in this paper.

A performance evaluation of four parallel join algorithms in a shared-nothing multiprocessor environment

Abstract: In this paper we analyze and compare four parallel join algorithms. Grace and Hybrid hash represent the class of hash-based join methods, Simple hash represents a looping algorithm with hashing, and our last algorithm is the more traditional sort-merge. The performance of each of the algorithms with different tuple distribution policies, the addition of bit vector filters, varying amounts of main-memory for joining, and non-uniformly distributed join attribute values is studied. The Hybrid hash-join algorithm is found to be superior except when the join attribute values of the inner relation are non-uniformly distributed and memory is limited. In this case, a more conservative algorithm such as the sort-merge algorithm should be used. The Gamma database machine serves as the host for the performance comparison.

Supporting top- k join queries in relational databases

Abstract: Ranking queries, also known as top-k queries, produce results that are ordered on some computed score. Typically, these queries involve joins, where users are usually interested only in the top-k join results. Top-k queries are dominant in many emerging applications, e.g., multimedia retrieval by content, Web databases, data mining, middlewares, and most information retrieval applications. Current relational query processors do not handle ranking queries efficiently, especially when joins are involved. In this paper, we address supporting top-k join queries in relational query processors. We introduce a new rank-join algorithm that makes use of the individual orders of its inputs to produce join results ordered on a user-specified scoring function. The idea is to rank the join results progressively during the join operation. We introduce two physical query operators based on variants of ripple join that implement the rank-join algorithm. The operators are nonblocking and can be integrated into pipelined execution plans. We also propose an efficient heuristic designed to optimize a top-k join query by choosing the best join order. We address several practical issues and optimization heuristics to integrate the new join operators in practical query processors. We implement the new operators inside a prototype database engine based on PREDATOR. The experimental evaluation of our approach compares recent algorithms for joining ranked inputs and shows superior performance.