Join processing in database systems with large main memories
ACM Transactions on Database Systems (TODS)
SIGMOD '86 Proceedings of the 1986 ACM SIGMOD international conference on Management of data
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
An incremental join attachment for Starburst
Proceedings of the sixteenth international conference on Very large databases
A compression technique to materialize transitive closure
ACM Transactions on Database Systems (TODS)
Computing a maximum cardinality matching in a bipartite graph in time On1.5m/logn
Information Processing Letters
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
Bipartite graphs and their applications
Bipartite graphs and their applications
Journal of the ACM (JACM)
A modification of Warshall's algorithm for the transitive closure of binary relations
Communications of the ACM
On supporting containment queries in relational database management systems
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Efficient subtyping tests with PQ-encoding
OOPSLA '01 Proceedings of the 16th ACM SIGPLAN conference on Object-oriented programming, systems, languages, and applications
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
IEEE Transactions on Knowledge and Data Engineering
Object-Oriented Database Systems: Promises, Reality, and Future
VLDB '93 Proceedings of the 19th International Conference on Very Large Data Bases
On the Graph Traversal and Linear Binary-Chain Programs
IEEE Transactions on Knowledge and Data Engineering
Reachability and Distance Queries via 2-Hop Labels
SIAM Journal on Computing
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
Dual Labeling: Answering Graph Reachability Queries in Constant Time
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Fast computation of reachability labeling for large graphs
EDBT'06 Proceedings of the 10th international conference on Advances in Database Technology
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Let G(V, E) be a digraph (directed graph) with n nodes and e edges. Digraph G* = (V, E*) is the reflexive, transitive closure of G if (v, u) ∈ E* iff there is a path from v to u in G. If we store it as a matrix, O(n2) space is required, not suitable for large graphs. In this paper, we present a new method to reduce the space overhead to O(bn), where b is the G's width, defined to be the size of a largest node subset U of G such that for every pair of nodes u, v ∈ U, there does not exist a path from u to v or from v to u. With such a compressed data structure of transitive closure, the time for checking reachability (whether a node is reachable from another node through a path) is bounded by O(logb). In addition, this data structure can be generated in O(be') time, where e' is the size of a subset of E, which contains only those edges (u, v) such that there is no path of length ≥2 connecting u and v. We are able to show that the average value of e' is on the order of O(n1.5). Our method is suitable for both acyclic and cyclic graphs.