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Algorithms, Graph Theory, and the Solution of Laplacian Linear Equations

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Automata, Languages, and Programming (ICALP 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7392))

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Abstract

In this talk, we survey major developments in the design of algorithms for solving Laplacian linear equations, by which we mean systems of linear equations in the Laplacian matrices of graphs and their submatrices. We begin with a few examples of where such equations arise, including the analysis of networks of resistors, the analysis of networks of springs, and the solution of maximum flow problems by interior point methods.

This work is supported in part by the National Science Foundation under Grant Nos. 0915487 and 1111257.

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Author information

Authors and Affiliations

  1. Departments of Computer Science and Mathematics, Program in Applied Mathematics, Yale University, USA

    Daniel A. Spielman

Authors
  1. Daniel A. Spielman
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Centre for Discrete Mathematics and its Applications, University of Warwick, Warwick, UK

    Artur Czumaj

  2. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Kurt Mehlhorn

  3. Computer Laboratory,, University of Cambridge, UK

    Andrew Pitts

  4. ETH Zurich, Switzerland

    Roger Wattenhofer

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Spielman, D.A. (2012). Algorithms, Graph Theory, and the Solution of Laplacian Linear Equations. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds) Automata, Languages, and Programming. ICALP 2012. Lecture Notes in Computer Science, vol 7392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31585-5_5

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  • DOI: https://doi.org/10.1007/978-3-642-31585-5_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31584-8

  • Online ISBN: 978-3-642-31585-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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