An O(|V||E|) algorithm for finding immediate multiple-vertex dominators

• Published in: Information processing letters Vol. 59; no. 1; pp. 9 - 11
• Main Authors: ALSTRUP, S, CLAUSEN, J, JØRGENSEN, K
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Science 08.07.1996; Elsevier Sequoia S.A
• Subjects: Algorithmics. Computability. Computer arithmetics; Algorithms; Applied sciences; Computer science; control theory; systems; Exact sciences and technology; Graphs; Information processing; Information retrieval. Graph; Optimization; Studies; Theoretical computing; Vertex(graph); Graph theory; Algorithms
• ISSN: 0020-0190; 1872-6119
• DOI: 10.1016/0020-0190(96)00085-3

Finding dominators in a graph has been investigated in many papers in connection with global flow analysis and program optimization. Recently Gupta (1992) extended the problem to find generalized dominators, which can be used for example, for propagating loop invariant statements out of the loop in cases where no single vertex dominates the loop exit, but where a union of vertices together dominates the exit. Fundamental in connection with generalized dominators are the immediate multiple-vertex dominators. An O(absolute value of V * absolute value of E) algorithm for finding immediate multiple-vertex dominators in a graph with vertices V and edges E is presented.