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RANDOM
Two-Sided Lossless Expanders in the Unbalanced Setting

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

Published in: LIPIcs, Volume 392, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)


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.

Cite as

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)


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@InProceedings{chattopadhyay_et_al:LIPIcs.APPROX/RANDOM.2026.34,
  author =	{Chattopadhyay, Eshan and Gurumukhani, Mohit and Ringach, Noam and Zhao, Yunya},
  title =	{{Two-Sided Lossless Expanders in the Unbalanced Setting}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2026)},
  pages =	{34:1--34:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-449-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{392},
  editor =	{Singh, Mohit and Gur, Tom},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2026.34},
  URN =		{urn:nbn:de:0030-drops-277517},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2026.34},
  annote =	{Keywords: Pseudorandomness, lossless expanders, multiplicity codes, condensers}
}

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