Operations on sparse relations

  • Authors:
  • H. B. Hunt, III;J. D. Ullman;T. G. Szymanski

  • Affiliations:
  • Harvard Univ., Cambridge, MA;Princeton Univ., Princeton, NJ;-

  • Venue:
  • Communications of the ACM
  • Year:
  • 1977

Quantified Score

Hi-index 48.22

Visualization

Abstract

Various computations on relations, Boolean matrices, or directed graphs, such as the computation of precedence relations for a context-free grammar, can be done by a practical algorithm that is asymptotically faster than those in common use. For example, how to compute operator precedence or Wirth-Weber precedence relations in O(n2) steps is shown, as well as how to compute linear precedence functions in O(n) steps, where n is the size of a grammar. The heart of the algorithms is a general theorem giving sufficient conditions under which an expression whose operands are sparse relations and whose operators are composition, transitive closure, union, and inverse, can be computed efficiently.