Dominators, Directed Bipolar Orders, and Independent Spanning Trees

  • Loukas Georgiadis
  • Robert E. Tarjan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7391)


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.


Span Tree Dominator Tree Valid Tree Independent Span Tree Proper Descendant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Loukas Georgiadis
    • 1
  • Robert E. Tarjan
    • 2
    • 3
  1. 1.Department of Computer ScienceUniversity of IoanninaGreece
  2. 2.Department of Computer SciencePrinceton UniversityPrincetonUSA
  3. 3.Hewlett-Packard LaboratoriesUSA

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