Graph algorithms and NP-completeness
Graph algorithms and NP-completeness
Join processing in database systems with large main memories
ACM Transactions on Database Systems (TODS)
An amateur's introduction to recursive query processing strategies
SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
A data management extension architecture
SIGMOD '87 Proceedings of the 1987 ACM SIGMOD international conference on Management of data
Amortized efficiency of a path retrieval data structure
Theoretical Computer Science
Clustering a DAG for CAD Databases
IEEE Transactions on Software Engineering
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)
Hybrid transitive closure algorithms
Proceedings of the sixteenth international conference on Very large databases
A compression technique to materialize transitive closure
ACM Transactions on Database Systems (TODS)
Type-extension type test can be performed in constant time
ACM Transactions on Programming Languages and Systems (TOPLAS)
Efficient assembly for complex objects
SIGMOD '91 Proceedings of the 1991 ACM SIGMOD international conference on Management of data
ACM Transactions on Database Systems (TODS)
Transitive closure algorithms based on graph traversal
ACM Transactions on Database Systems (TODS)
A performance study of transitive closure algorithms
SIGMOD '94 Proceedings of the 1994 ACM SIGMOD international conference on Management of data
Layered index structures in document database systems
Proceedings of the seventh international conference on Information and knowledge management
Journal of the ACM (JACM)
A modification of Warshall's algorithm for the transitive closure of binary relations
Communications of the ACM
Efficient subtyping tests with PQ-encoding
OOPSLA '01 Proceedings of the 16th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
On extending the functions of a relational database system
SIGMOD '82 Proceedings of the 1982 ACM SIGMOD international conference on Management of data
The Implementation of POSTGRES
IEEE Transactions on Knowledge and Data Engineering
Path Signatures: A Way to Speed Up Recursion in Relational Databases
IEEE Transactions on Knowledge and Data Engineering
Path Dictionary: A New Access Method for Query Processing in Object-Oriented Databases
IEEE Transactions on Knowledge and Data Engineering
IEEE Transactions on Knowledge and Data Engineering
Implementation Techniques of Complex Objects
VLDB '86 Proceedings of the 12th International Conference on Very Large Data Bases
Object-Oriented Database Systems: Promises, Reality, and Future
VLDB '93 Proceedings of the 19th International Conference on Very Large Data Bases
Maintenance of Transitive Closures and Transitive Reductions of Graphs
WG '87 Proceedings of the International Workshop on Graph-Theoretic Concepts in Computer Science
On Incremental Computation of Transitive Closure and Greedy Alignment
CPM '97 Proceedings of the 8th Annual Symposium on Combinatorial Pattern Matching
Materialization and Incremental Update of Path Information
Proceedings of the Fifth International Conference on Data Engineering
On the Graph Traversal and Linear Binary-Chain Programs
IEEE Transactions on Knowledge and Data Engineering
Amortized efficiency of list update rules
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Decomposing DAGs into disjoint chains
DEXA'07 Proceedings of the 18th international conference on Database and Expert Systems Applications
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A composite object represented as a directed graph (digraph for short) is an important data structure that requires efficient support in CAD/CAM, CASE, office systems, software management, web databases, and document databases. It is cumbersome to handle such objects in relational database systems when they involve ancestor-descendant relationships (or say, recursive relationships). In this paper, we present a new encoding method to label a digraph, which reduces the footprints of all previous strategies. This method is based on a tree labeling method and the concept of branchings that are used in graph theory for finding the shortest connection networks. A branching is a subgraph of a given digraph that is in fact a forest, but covers all the nodes of the graph. On the one hand, the proposed encoding scheme achieves the smallest space requirements among all previously published strategies for recognizing recursive relationships. On the other hand, it leads to a new algorithm for computing transitive closures for DAGs (directed acyclic graph) in O(e·b) time and O(n·b) space, where n represents the number of the nodes of a DAG, e the numbers of the edges, and b the DAG's breadth. The method can also be extended to graphs containing cycles. Especially, based on this encoding method, a multi-level compression is developed, by means of which the space for the representation of a transitive closure can be reduced to O((b/dk)·n), where k is the number of compression levels and d is the average outdegree of the nodes.