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Fast Convolutions for Near-Convex Sequences

Authors Cornelius Brand , Alexandra Lassota



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Cornelius Brand
  • Institute of Logic and Computation, Vienna University of Technology, Austria
Alexandra Lassota
  • Max Planck Institute for Informatics, SIC, Saarbrücken, Germany

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Cornelius Brand and Alexandra Lassota. Fast Convolutions for Near-Convex Sequences. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 16:1-16:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ISAAC.2023.16

Abstract

We develop algorithms for (min,+)-Convolution and related convolution problems such as Super Additivity Testing, Convolution 3-Sum and Minimum Consecutive Subsums which use the degree of convexity of the instance as a parameter. Assuming the min-plus conjecture (Künnemann-Paturi-Schneider, ICALP'17 and Cygan et al., ICALP'17), our results interpolate in an optimal manner between fully convex instances, which can be solved in near-linear time using Legendre transformations, and general non-convex sequences, where the trivial quadratic-time algorithm is conjectured to be best possible, up to subpolynomial factors.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
Keywords
  • (min,+)-convolution
  • fine-grained complexity
  • convex sequences

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