Two graph algorithms derived

Abstract.

Much emphasis has been placed in recent years on deriving or calculating programs rather than proving them correct. Adequate calculational frameworks are needed to support such an approach. The present work explores the use of a calculus of relations to express and reason about graph properties in an algorithmic context. We first construct a generic program that computes a maximal set, over some universe, satisfying a certain given predicate. The development is presented as a step-by-step derivation, applying well-known techniques and heuristics that aid the construction of imperative programs. A calculational framework of relations is then used to obtain two instances of the generic program. These instances correspond to the computation of maximal graph components, viz. maximal independent sets of vertices and maximal sets of edges without cycles (i.e. maximal forests).