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Computer Science > Data Structures and Algorithms

arXiv:2510.21613 (cs)
[Submitted on 24 Oct 2025]

Title:Beyond Smoothed Analysis: Analyzing the Simplex Method by the
Book

Authors:Eleon Bach, Alexander E. Black, Sophie Huiberts, Sean Kafer
View a PDF of the paper titled Beyond Smoothed Analysis: Analyzing
the Simplex Method by the Book, by Eleon Bach and Alexander E. Black
and Sophie Huiberts and Sean Kafer
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    Abstract:Narrowing the gap between theory and practice is a
    longstanding goal of the algorithm analysis community. To further
    progress our understanding of how algorithms work in practice, we
    propose a new algorithm analysis framework that we call by the
    book analysis. In contrast to earlier frameworks, by the book
    analysis not only models an algorithm's input data, but also the
    algorithm itself. Results from by the book analysis are meant to
    correspond well with established knowledge of an algorithm's
    practical behavior, as they are meant to be grounded in
    observations from implementations, input modeling best practices,
    and measurements on practical benchmark instances. We apply our
    framework to the simplex method, an algorithm which is beloved
    for its excellent performance in practice and notorious for its
    high running time under worst-case analysis. The simplex method
    similarly showcased the state of the art framework smoothed
    analysis (Spielman and Teng, STOC'01). We explain how our
    framework overcomes several weaknesses of smoothed analysis and
    we prove that under input scaling assumptions, feasibility
    tolerances and other design principles used by simplex method
    implementations, the simplex method indeed attains a polynomial
    running time.

Comments: 42 pages
Subjects: Data Structures and Algorithms (cs.DS); Optimization and
          Control (math.OC)
Cite as:  arXiv:2510.21613 [cs.DS]
          (or arXiv:2510.21613v1 [cs.DS] for this version)
          https://doi.org/10.48550/arXiv.2510.21613
          Focus to learn more
          arXiv-issued DOI via DataCite (pending registration)

Submission history

From: Alexander Black [view email]
[v1] Fri, 24 Oct 2025 16:17:47 UTC (59 KB)
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    Analyzing the Simplex Method by the Book, by Eleon Bach and
    Alexander E. Black and Sophie Huiberts and Sean Kafer
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