Operations on sparse relations
Harry B. Hunt, Jeffrey David Ullman, Thomas G. Szymanski · Communications of the ACM · 1977
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(n 2 ) 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.