Abstract
We consider problems related to dominators and independent spanning trees in flowgraphs and provide linear-time algorithms for their solutions. We introduce the notion of a directed bipolar order, generalizing a previous notion of Plein and Cheriyan and Reif. We show how to construct such an order from information computed by several known algorithms for finding dominators. We show how to concurrently verify the correctness of a dominator tree D and a directed bipolar order O very simply, and how to construct from D and O two spanning trees whose paths are disjoint except for common dominators. Finally, we describe alternative ways to verify dominators without using a directed bipolar order.
Research at the University of Ioannina partially funded by the John S. Latsis Public Benefit Foundation. The sole responsibility for the content of this paper lies with its authors. Research at Princeton University partially supported by NSF grants CCF-0830676 and CCF-0832797. Research while visiting Stanford University partially supported by an AFOSR MURI grant. The information contained herein does not necessarily reflect the opinion or policy of the federal government and no official endorsement should be inferred.
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Georgiadis, L., Tarjan, R.E. (2012). Dominators, Directed Bipolar Orders, and Independent Spanning Trees. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7391. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31594-7_32
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