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
Dynamic reachability in planar digraphs with one source and one sink
Theoretical Computer Science
An Efficient Data Structure for Lattice Operations
SIAM Journal on Computing
Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
Compact oracles for reachability and approximate distances in planar digraphs
Journal of the ACM (JACM)
Dominator tree verification and vertex-disjoint paths
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Dual Labeling: Answering Graph Reachability Queries in Constant Time
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Computing Frequency Dominators and Related Problems
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
Testing 2-vertex connectivity and computing pairs of vertex-disjoint s-t paths in digraphs
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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For a given collection G of directed graphs we define the joinreachability graph of G, denoted by J (G), as the directed graph that, for any pair of vertices a and b, contains a path from a to b if and only if such a path exists in all graphs of G. Our goal is to compute an efficient representation of J (G). In particular, we consider two versions of this problem. In the explicit version we wish to construct the smallest joinreachability graph for G. In the implicit version we wish to build an efficient data structure (in terms of space and query time) such that we can report fast the set of vertices that reach a query vertex in all graphs of G. This problem is related to the well-studied reachability problem and is motivated by emerging applications of graph-structured databases and graph algorithms. We consider the construction of join-reachability structures for two graphs and develop techniques that can be applied to both the explicit and the implicit problem. First we present optimal and near-optimal structures for paths and trees. Then, based on these results, we provide efficient structures for planar graphs and general directed graphs.