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Loop Nesting Forests, Dominators, and Applications

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Experimental Algorithms (SEA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8504))

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Abstract

Loop nesting forests and dominator trees are important tools in program optimization and code generation, and they have applications in other diverse areas. In this work we first present carefully engineered implementations of efficient algorithms for computing a loop nesting forest of a given directed graph, including a very efficient algorithm that computes the forest in a single depth-first search. Then we revisit the problem of computing dominators and present efficient implementations of the algorithms recently proposed by Fraczak et al. [12], which include an algorithm for acyclic graphs and an algorithm that computes both the dominator tree and a loop nesting forest. We also propose a new algorithm than combines the algorithm of Fraczak et al. for acyclic graphs with the algorithm of Lengauer and Tarjan. Finally, we provide fast algorithms for the following related problems: computing bridges and testing 2-edge connectivity, verifying dominators and testing 2-vertex connectivity, and computing a low-high order and two independent spanning trees. We exhibit the efficiency of our algorithms experimentally on large graphs taken from a variety of application areas.

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Author information

Authors and Affiliations

  1. Department of Computer Science & Engineering, University of Ioannina, Greece

    Loukas Georgiadis & Nikos Parotsidis

  2. Department of Computer, Control, and Management Engineering and Research Centre for Transport and Logistics, “Sapienza” Università di Roma, Italy

    Luigi Laura

  3. Department of Computer Science, Princeton University, USA

    Robert E. Tarjan

  4. Microsoft Research, Silicon Valley, USA

    Robert E. Tarjan

Authors
  1. Loukas Georgiadis
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  2. Luigi Laura
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  3. Nikos Parotsidis
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  4. Robert E. Tarjan
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Editor information

Editors and Affiliations

  1. School of IT, University of Sydney, Building J12, 2006, Sydney, NSW, Australia

    Joachim Gudmundsson

  2. Department of Computer Science, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen East, Denmark

    Jyrki Katajainen

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Georgiadis, L., Laura, L., Parotsidis, N., Tarjan, R.E. (2014). Loop Nesting Forests, Dominators, and Applications. In: Gudmundsson, J., Katajainen, J. (eds) Experimental Algorithms. SEA 2014. Lecture Notes in Computer Science, vol 8504. Springer, Cham. https://doi.org/10.1007/978-3-319-07959-2_15

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  • DOI: https://doi.org/10.1007/978-3-319-07959-2_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07958-5

  • Online ISBN: 978-3-319-07959-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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