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
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
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
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
Graph Algorithms
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 labeling schemes for the semantic web
WWW '03 Proceedings of the 12th international conference on World Wide Web
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
An Efficient Algorithm for Answering Graph Reachability Queries
ICDE '08 Proceedings of the 2008 IEEE 24th 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
GRAIL: scalable reachability index for large graphs
Proceedings of the VLDB Endowment
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Graph reachability is fundamental to a wide range of applications, including CAD/CAM, CASE, office systems, software management, as well as geographical navigation and internet routing. Many applications involve huge graphs and requires fast answering of reachability queries. Several reachability labeling methods have been proposed for this purpose. They assign labels to the nodes, such that the reachability between any two nodes can be determined using their labels only. In this paper, we propose a new data structure, called a general spanning tree of a directed acyclic graph (DAG) to minimize label space. Different from a traditional spanning tree, an edge in a general spanning tree T of a DAG G may corresponds to a path in G. That is, for each edge u → v in T, we have a path from u to v in G. An algorithm is discussed to find such a tree with the least number of leaf nodes in O(bn √b) time, where n is the number of the nodes of G, and b is the number of the leaf nodes of T. It can be proven that b equals 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. Based on T, we are able to reduce the label space to O(bn) with O(logb) reachability query time. Our method can also be extended for graphs containing cycles.