Incremental FO( +, < ) Maintenance of All-Pairs Shortest Paths for Undirected Graphs after Insertions and Deletions
We give incremental algorithms, which support both edge insertions and deletions, for the all-pairs shortest-distance problem (APSD) in weighted undirected graphs. Our algorithms use first-order queries, + (addition) and < (less-than); they store O(n 2) number of tuples, where n is the number of vertices, and have AC 0 data complexity for integer weights. Since FO(+,<) is supported by almost all current database systems, our maintenance algorithms are more appropriate for database applications than non-database query type of maintenance algorithms. Our algorithms can also be extended to duplicate semantics.
Unable to display preview. Download preview PDF.
- J. A. Blakeley, P.-A. Larson, and F. W. Tompa. Efficiently updating materialized views. In Proc. ACM SIGMOD Int. Conf. on Management of Data, pages 61–71, 1986.Google Scholar
- A. L. Buchsbaum, P. C. Kanellakis, and J. S. Vitter. A data structure for arc insertion and regular path finding. In Proc. ACM-SIAM Symp. on Discrete Algorithms, 1990.Google Scholar
- Hristo N. Djidjev, Grammati E. Pantziou, and Christos D. Zaroliagis. On-line and dynamic algorithms for shortest path problems. In STACS: Annual Symposium on Theoretical Aspects of Computer Science, 1995.Google Scholar
- G. Dong and J. Su. Space bounded FOIES. In Proc. of the ACM Symposium on Principles of Database Systems, pages 139–150, mtMay 1995.Google Scholar
- G. Dong and R. Topor. Incremental evaluation of datalog queries. In Proc. Int’l Conference on Database Theory, pages 282–296, Berlin, Germany, October 1992.Google Scholar
- Guozhu Dong and Ramamohanarao Kotagiri. Incrementally evaluating constrained transitive closure by conjunctive querie. In International Conference on Deductive and Object-Oriented Databases, 1997.Google Scholar
- S. Grumbach and J. Su. First-order definability over constraint databases. In Proceedings of Conference on Constraint Programming, 1995.Google Scholar
- Philip N. Klein, Satish Rao, Monika H. Rauch, and S. Subramanian. Faster shortest-path algorithms for planar graphs. In Proc. 26th Symp. Theory of Computing, pages 27–37. Assoc. for Computing Machinery, 1994.Google Scholar
- Chaoyi Pang. Incremental Maintenance Reachability of Graph in First-order and Its extension. PhD thesis, The University of Melbourne, 1999.Google Scholar
- Sushant Patnaik and Neil Immerman. Dyn-FO: A parallel dynamic complexity class. In Proc. ACM Symp. on Principles of Database Systems, pages 210–221, 1994.Google Scholar