The paper presents a known sequential and a new parallel/concurrent actor-oriented solution of the Dominator problem. The new parallel/concurrent actor-oriented Dominator algorithm computes sets of dominators of nodes of a given control flow graph in a parallel/concurrent actor oriented way. The new Dominator algorithm is implemented as the multi-actor system in the Easel programming language. The new Dominator algorithm and its implementation are important contributions to the theory and practice of parallel / concurrent algorithms and actor-oriented programming. Because Dominator algorithm has applications in Information Assurance and Computer Security in detecting and locating program attacks – this novel and innovative Dominator algorithm may greatly influence these disciplines.