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Two-Sided Lossless Expanders in the Unbalanced Setting

Authors Eshan Chattopadhyay , Mohit Gurumukhani , Noam Ringach , Yunya Zhao

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ACM Subject Classification
  • Theory of computation → Expander graphs and randomness extractors
Keywords
  • Pseudorandomness
  • lossless expanders
  • multiplicity codes
  • condensers

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Abstract

We present the first explicit construction of two-sided lossless expanders in the unbalanced setting (bipartite graphs that have polynomially many more nodes on the left than on the right). Prior to our work, all known explicit constructions in the unbalanced setting achieved only one-sided lossless expansion.
Specifically, we show that the one-sided lossless expanders constructed by Kalev and Ta-Shma (RANDOM'22) - that are based on multiplicity codes introduced by Kopparty, Saraf, and Yekhanin (STOC'11) - are, in fact, two-sided lossless expanders. Moreover, we show that our result is tight, thus completely characterizing the graph of Kalev and Ta-Shma.

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Eshan Chattopadhyay, Mohit Gurumukhani, Noam Ringach, and Yunya Zhao. Two-Sided Lossless Expanders in the Unbalanced Setting. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 392, pp. 34:1-34:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2026.34

Author Details

Eshan Chattopadhyay
  • Cornell University, Ithaca, NY, USA
Mohit Gurumukhani
  • Cornell University, Ithaca, NY, USA
Noam Ringach
  • Cornell University, Ithaca, NY, USA
Yunya Zhao
  • Cornell University, Ithaca, NY, USA

Funding

  • Chattopadhyay, Eshan: Supported by a Sloan Research Fellowship, NSF CAREER Award 2045576 and NSF Award CCF-2514586.
  • Gurumukhani, Mohit: Supported by a Sloan Research Fellowship, NSF CAREER Award 2045576 and NSF Award CCF-2514586.
  • Ringach, Noam: Supported by NSF GRFP grant DGE – 2139899, NSF CAREER Award 2045576, a Sloan Research Fellowship and NSF Award CCF-2514586.
  • Zhao, Yunya: Supported by a Sloan Research Fellowship, NSF CAREER Award 2045576 and NSF Award CCF-2514586.

Acknowledgements

We would like to thank Itay Kalev for helpful feedback on our paper. We are also grateful to insightful suggestions from anonymous reviewers that led to simplifying some of our proofs.

References

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