Hard submatrices for non-negative rank and communication complexity

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00599140" target="_blank" >RIV/67985840:_____/24:00599140 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.4230/LIPIcs.CCC.2024.13" target="_blank" >https://doi.org/10.4230/LIPIcs.CCC.2024.13</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.CCC.2024.13" target="_blank" >10.4230/LIPIcs.CCC.2024.13</a>

Result language

angličtina

Original language name

Hard submatrices for non-negative rank and communication complexity

Original language description

Given a non-negative real matrix M of non-negative rank at least r, can we witness this fact by a small submatrix of M? While Moitra (SIAM J. Comput. 2013) proved that this cannot be achieved exactly, we show that such a witnessing is possible approximately: an m × n matrix of non-negative rank r always contains a submatrix with at most r3 rows and columns with non-negative rank at least Ω(log nrlog m). A similar result is proved for the 1-partition number of a Boolean matrix and, consequently, also for its two-player deterministic communication complexity. Tightness of the latter estimate is closely related to the log-rank conjecture of Lovász and Saks.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

<a href="/en/project/GX19-27871X" target="_blank" >GX19-27871X: Efficient approximation algorithms and circuit complexity</a><br>

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

39th Computational Complexity Conference (CCC 2024)

ISBN

978-3-95977-331-7

ISSN

1868-8969

e-ISSN

1868-8969

Number of pages

12

Pages from-to

13

Publisher name

Schloss Dagstuhl, Leibniz-Zentrum für Informatik

Place of publication

Dagstuhl

Event location

Ann Arbor

Event date

Jul 22, 2024

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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