Better Space-Time-Robustness Trade-Offs for Set Reconciliation

Authors Djamal Belazzougui , Gregory Kucherov , Stefan Walzer

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Author Details

Djamal Belazzougui
  • CAPA, DTISI, Centre de Recherche sur l'Information Scientifique et Technique, Algiers, Algeria
Gregory Kucherov
  • LIGM, CNRS, Université Gustave Eiffel, Marne-la-Vallée, France
Stefan Walzer
  • Karlsruhe Institute of Technology, Germany

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Djamal Belazzougui, Gregory Kucherov, and Stefan Walzer. Better Space-Time-Robustness Trade-Offs for Set Reconciliation. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 20:1-20:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


We consider the problem of reconstructing the symmetric difference between similar sets from their representations (sketches) of size linear in the number of differences. Exact solutions to this problem are based on error-correcting coding techniques and suffer from a large decoding time. Existing probabilistic solutions based on Invertible Bloom Lookup Tables (IBLTs) are time-efficient but offer insufficient success guarantees for many applications. Here we propose a tunable trade-off between the two approaches combining the efficiency of IBLTs with exponentially decreasing failure probability. The proof relies on a refined analysis of IBLTs proposed in (Bæk Tejs Houen et al. SOSA 2023) which has an independent interest. We also propose a modification of our algorithm that enables telling apart the elements of each set in the symmetric difference.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • Theory of computation → Randomness, geometry and discrete structures
  • Theory of computation → Sketching and sampling
  • Theory of computation → Error-correcting codes
  • data structures
  • hashing
  • set reconciliation
  • invertible Bloom lookup tables
  • random hypergraphs
  • BCH codes


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