1 Search Results for "Ignatiev, Artur"

Document
DOI: 10.4230/LIPIcs.ISAAC.2022.66
Super-Cubic Lower Bound for Generalized Karchmer-Wigderson Games

Authors: Artur Ignatiev, Ivan Mihajlin, and Alexander Smal

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
In this paper, we prove a super-cubic lower bound on the size of a communication protocol for generalized Karchmer-Wigderson game for an explicit function f: {0,1}ⁿ → {0,1}^{log n}. Lower bounds for original Karchmer-Wigderson games correspond to De Morgan formula lower bounds, thus the best known size lower bound is cubic. The generalized Karchmer-Wigderson games are similar to the original ones, so we hope that our approach can provide an insight for proving better lower bounds on the original Karchmer-Wigderson games, and hence for proving new lower bounds on De Morgan formula size. To achieve super-cubic lower bound we adapt several techniques used in formula complexity to communication protocols, prove communication complexity lower bound for a composition of several functions with a multiplexer relation, and use a technique from [Ivan Mihajlin and Alexander Smal, 2021] to extract the "hardest" function from it. As a result, in this setting we are able to show that there is a relatively small set of functions such that at least one of them does not have a small protocol. The resulting lower bound of Ω̃(n^3.156) is significantly better than the bound obtained from the counting argument.
Cite as

Artur Ignatiev, Ivan Mihajlin, and Alexander Smal. Super-Cubic Lower Bound for Generalized Karchmer-Wigderson Games. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 66:1-66:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{ignatiev_et_al:LIPIcs.ISAAC.2022.66,
  author =	{Ignatiev, Artur and Mihajlin, Ivan and Smal, Alexander},
  title =	{{Super-Cubic Lower Bound for Generalized Karchmer-Wigderson Games}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{66:1--66:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.66},
  URN =		{urn:nbn:de:0030-drops-173510},
  doi =		{10.4230/LIPIcs.ISAAC.2022.66},
  annote =	{Keywords: communication complexity, circuit complexity, Karchmer-Wigderson games}
}
  • Refine by Author
  • 1 Ignatiev, Artur
  • 1 Mihajlin, Ivan
  • 1 Smal, Alexander

  • Refine by Classification
  • 1 Theory of computation → Circuit complexity

  • Refine by Keyword
  • 1 Karchmer-Wigderson games
  • 1 circuit complexity
  • 1 communication complexity

  • Refine by Type
  • 1 document

  • Refine by Publication Year
  • 1 2022

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact