On compiling queries in recursive first-order databases
Journal of the ACM (JACM)
An amateur's introduction to recursive query processing strategies
SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
Traversal recursion: a practical approach to supporting recursive applications
SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
Relational Information Systems
Relational Information Systems
A study of transitive closure as a recursion mechanism
SIGMOD '87 Proceedings of the 1987 ACM SIGMOD international conference on Management of data
Design of an external schema facility to define and process recursive structures
ACM Transactions on Database Systems (TODS)
Equivalence of Relational Algebra and Relational Calculus Query Languages Having Aggregate Functions
Journal of the ACM (JACM)
Logic and Databases: A Deductive Approach
ACM Computing Surveys (CSUR)
A relational model of data for large shared data banks
Communications of the ACM
Principles of Database Systems
Principles of Database Systems
Universality of data retrieval languages
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Horn clauses and the fixpoint query hierarchy
PODS '82 Proceedings of the 1st ACM SIGACT-SIGMOD symposium on Principles of database systems
An optimizing prolog front-end to a relational query system
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
Moving Selections into Linear Least Fixpoint Queries
Proceedings of the Fourth International Conference on Data Engineering
Direct Algorithms for Computing the Transitive Closure of Database Relations
VLDB '87 Proceedings of the 13th International Conference on Very Large Data Bases
Efficient Search in Very Large Databases
VLDB '88 Proceedings of the 14th International Conference on Very Large Data Bases
New features for a relational database system to support computer aided design
New features for a relational database system to support computer aided design
Pattern-based and knowledge-directed query compilation for recursive data bases (expert, systems, reductive, logic)
Theory of Relational Databases
Theory of Relational Databases
Multiprocessor transitive closure algorithms
DPDS '88 Proceedings of the first international symposium on Databases in parallel and distributed systems
ODE (Object Database and Environment): the language and the data model
SIGMOD '89 Proceedings of the 1989 ACM SIGMOD international conference on Management of data
Efficient management of transitive relationships in large data and knowledge bases
SIGMOD '89 Proceedings of the 1989 ACM SIGMOD international conference on Management of data
Direct transitive closure algorithms: design and performance evaluation
ACM Transactions on Database Systems (TODS)
IEEE Transactions on Software Engineering - Special issue: specification and analysis of real-time systems
Extending SQL with General Transitive Closure and Extreme Value Selections
IEEE Transactions on Knowledge and Data Engineering
Object-Oriented Query Languages: The Notion and the Issues
IEEE Transactions on Knowledge and Data Engineering
The ρ operator: discovering and ranking associations on the semantic web
ACM SIGMOD Record
Distributed Transitive Closure Computations: The Disconnection Set Approach
VLDB '90 Proceedings of the 16th International Conference on Very Large Data Bases
Hybrid Transitive Closure Algorithms
VLDB '90 Proceedings of the 16th International Conference on Very Large Data Bases
Ρ-Queries: enabling querying for semantic associations on the semantic web
WWW '03 Proceedings of the 12th international conference on World Wide Web
Declarative routing: extensible routing with declarative queries
Proceedings of the 2005 conference on Applications, technologies, architectures, and protocols for computer communications
The expressivity of XPath with transitive closure
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Extending SPARQL with regular expression patterns (for querying RDF)
Web Semantics: Science, Services and Agents on the World Wide Web
A magic approach to optimizing incremental relational expressions
IDEAS '09 Proceedings of the 2009 International Database Engineering & Applications Symposium
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An extension of E.F. Codd's relational algebra (1970) with an alpha operator is presented that allows a large class of natural and useful recursive queries to be expressed, and yet has the property of being efficiently implementable. Formally, this class is a superset of linear recursive queries. Intuitively, this class comprises queries that examine transitive relationships between various instances of an entity. It is believed that this class covers many natural and interesting recursive queries. Examples of such queries include determining parts requirements for manufacturing a product, finding the critical path in a project management network, finding the shortest path between two cities, verifying connectivity between two points of a circuit, etc.