Finding dominators via disjoint set union |
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Institution: | 1. Benbria Corporation, 390 March Road, Suite 110 Ottawa, Ontario K2K 0G7, Canada;2. Université du Québec en Outaouais, Gatineau, Québec, Canada;3. Department of Computer Science & Engineering, University of Ioannina, Greece;4. Department of Computer Science, Princeton University, Princeton, NJ, United States;5. Microsoft Research Silicon Valley, United States |
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Abstract: | The problem of finding dominators in a directed graph has many important applications, notably in global optimization of computer code. Although linear and near-linear-time algorithms exist, they use sophisticated data structures. We develop an algorithm for finding dominators that uses only a “static tree” disjoint set data structure in addition to simple lists and maps. The algorithm runs in near-linear or linear time, depending on the implementation of the disjoint set data structure. We give several versions of the algorithm, including one that computes loop nesting information (needed in many kinds of global code optimization) and that can be made self-certifying, so that the correctness of the computed dominators is very easy to verify. |
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Keywords: | Depth-first search Directed graph Disjoint set union Dominators Flow graph Global code optimization Program certification |
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