Better Space-Time-Robustness Trade-Offs for Set Reconciliation
Résumé
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 (Baek 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.
Mots clés
data structures
hashing
set reconciliation
invertible Bloom lookup tables
random hypergraphs
BCH codes
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
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