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A Simple Algorithm for Trimmed Multipoint Evaluation

Authors Nick Fischer , Melvin Kallmayer , Leo Wennmann

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LIPIcs.ESA.2025.89.pdf
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ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • Algebraic Algorithms
  • Multipoint Evaluation
  • Interpolation
  • LU Decomposition

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Abstract

Evaluating a polynomial on a set of points is a fundamental task in computer algebra. In this work, we revisit a particular variant called trimmed multipoint evaluation: given an n-variate polynomial with bounded individual degree d and total degree D, the goal is to evaluate it on a natural class of input points. This problem arises as a key subroutine in recent algorithmic results [Dinur; SODA '21], [Dell, Haak, Kallmayer, Wennmann; SODA '25]. It is known that trimmed multipoint evaluation can be solved in near-linear time [van der Hoeven, Schost; AAECC '13] by a clever yet somewhat involved algorithm. We give a simple recursive algorithm that avoids heavy computer-algebraic machinery, and can be readily understood by researchers without specialized background.

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Nick Fischer, Melvin Kallmayer, and Leo Wennmann. A Simple Algorithm for Trimmed Multipoint Evaluation. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 89:1-89:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ESA.2025.89

Author Details

Nick Fischer
  • INSAIT, Sofia University "St. Kliment Ohridski", Bulgaria
Melvin Kallmayer
  • Goethe University Frankfurt, Germany
Leo Wennmann
  • University of Southern Denmark, Odense, Denmark

Funding

  • Fischer, Nick: Partially funded by the Ministry of Education and Science of Bulgaria’s support for INSAIT as part of the Bulgarian National Roadmap for Research Infrastructure. Part of this work was done while the author was affiliated with the Weizmann Institute of Science.
  • Wennmann, Leo: Supported by Dutch Research Council (NWO) project "The Twilight Zone of Efficiency: Optimality of Quasi-Polynomial Time Algorithms" [grant number OCEN.W.21.268].

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