Yangjun Chen


The checking of graph reachability is an important opera¬tion in many applications, by which for two given nodes u and v in a directed graph G we will check whether u is reachable from v through a path in G or vice versa. In this paper, we focus ourselves on this issue. A new approach is proposed to compress transitive closure to support reach¬ability. The main idea is the concept of general spanning trees, as well as a new labeling technique, called core labeling. For a graph G with n nodes and e edges, the labeling time is bounded by O(n + e + tb), where t is the number of non-tree edges (edges that do not appear in the general spanning tree T 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. The space and time com¬plexities are bounded by O(n + tb) and O(logb), respectively.


  1. Agrawal, R., Borgida, A. and Jagadish, H.V., 1989. Efficient management of transtive relationships in large data and knowledge bases, Proc. of the 1989 ACM SIGMOD Intl. Conf. on Management of Data, Oregon, pp. 253-262.
  2. Y. Chen, Y., 2009. General Spanning Trees and Reachability Query Evaluation, in Proc. Canadian Conference on Computer Science and Software Engineering, ACM, Montreal, Canada, May 2009, pp. 243-252.
  3. J. Cheng, J., Yu, J.X., Lin, X., Wang, H. and Yu, P.S., 2006. Fast computation of reachability labeling for large graphs, in Proc. EDBT, Munich, Germany, May 26-31.
  4. Cohen, N.H., 1991. Type-extension tests can be performed in constant time, ACM Transactions on Programming Languages and Systems, 13:626-629.
  5. Cohen, E., Halperin, E., Kaplan, H. and Zwick, U., 2003. Reachability and distance queries via 2-hop labels, SIAM J. Comput, vol. 32, No. 5, pp. 1338-1355.
  6. Jagadish, H.V., 1990. “A Compression Technique to Materialize Transitive Closure,” ACM Trans. Database Systems, Vol. 15, No. 4, pp. 558 - 598.
  7. Knuth, D.E., 1969. The Art of Computer Programming, Vol.1, Addison-Wesley, Reading.
  8. R. Schenkel, R., Theobald, A. and G. Weikum, G., 2004. HOPI: an efficient connection index for complex XML document collections, in Proc. EDBT.
  9. R. Schenkel, R., Theobald, A, and G. Weikum, G., 2006. Efficient creation and incrementation maintenance of HOPI index for complex xml document collection, in Proc. ICDE.
  10. R. Tarjan, R., 1972. Depth-first Search and Linear Graph Algorithms, SIAM J. Compt. Vol. 1. No. 2, pp. 146 -140.
  11. Teuhola, J., 1996. Path Signatures: A Way to Speed up Recursion in Relational Databases, IEEE Trans. on Knowledge and Data Engineering, Vol. 8, No. 3, pp. 446 - 454.
  12. M. Thorup, M., 2004. “Compact Oracles for Reachability and Approximate Distances in Planar Digraphs,” JACM, 51, 6(Nov. 2004), 993-1024.
  13. Wang, H., He, H., Yang, J., Yu, P.S. and Yu, J.X., 2006. Dual Labeling: Answering Graph Reachability Queries in Constant time, in Proc. of Int. Conf. on Data Engineering, Atlanta, USA.
  14. Zibin, Y. and Gil, J., 2001. Efficient Subtyping Tests with PQ-Encoding, Proc. of the 2001 ACM SIGPLAN Conf. on Object-Oriented Programming Systems, Languages and Application, Florida, October 14-18, pp. 96-107.

Paper Citation

in Harvard Style

Chen Y. (2009). GENERAL SPANNING TREES AND CORE LABELING . In Proceedings of the 4th International Conference on Software and Data Technologies - Volume 1: ICSOFT, ISBN 978-989-674-009-2, pages 93-98. DOI: 10.5220/0002238500930098

in Bibtex Style

author={Yangjun Chen},
booktitle={Proceedings of the 4th International Conference on Software and Data Technologies - Volume 1: ICSOFT,},

in EndNote Style

JO - Proceedings of the 4th International Conference on Software and Data Technologies - Volume 1: ICSOFT,
SN - 978-989-674-009-2
AU - Chen Y.
PY - 2009
SP - 93
EP - 98
DO - 10.5220/0002238500930098