Incremental maintenance of shortest distance and transitive closure in first-order logic and SQL

  • Authors:
  • Chaoyi Pang;Guozhu Dong;Kotagiri Ramamohanarao

  • Affiliations:
  • CSIRO ICT Center/E-Health Research Center, Australia;Wright State University, Dayton, Ohio;University of Melbourne, Australia

  • Venue:
  • ACM Transactions on Database Systems (TODS)
  • Year:
  • 2005

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Abstract

Given a database, the view maintenance problem is concerned with the efficient computation of the new contents of a given view when updates to the database happen. We consider the view maintenance problem for the situation when the database contains a weighted graph and the view is either the transitive closure or the answer to the all-pairs shortest-distance problem (APSD). We give incremental algorithms for APSD, which support both edge insertions and deletions. For transitive closure, the algorithm is applicable to a more general class of graphs than those previously explored. Our algorithms use first-order queries, along with addition (+) and less-than (FO(+,O(n2) number of tuples, where n is the number of vertices, and have AC0 data complexity for integer weights. Since FO(+,