AbstractStatic Single-Assignment (SSA) form is an efficient intermediate representation used in virtual machines and modern compilers. It provides data flow information that simplifies the implementation of standard program optimisations such as constant propagation, dead code elimination, and partial redundancy elimination. Constructing SSA form involves the computation of graph relations such as dominance, and non-iterated and iterated dominance frontier. Although there exist efficient graph algorithms for these relations, the algorithms are elaborate to implement. In this paper we introduce a new approach to compute the dominance relation, the dominance frontiers, and the iterated dominance frontiers based on Boolean matrix calculus. We implemented our approach in an optimising backend for LCC bytecode and compared its performance with the state-of-the-art approaches. We use the Spec95 benchmark suite for our experimental evaluation.