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Partition expanders

SYSNO ASEP	0473687
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Partition expanders
Author(s)	Gavinsky, Dmitry (MU-W)_{RID, SAI, ORCID} Pudlák, Pavel (MU-W)_{RID, SAI}
Source Title	Theory of Computing Systems. - : Springer - ISSN 1432-4350 Roč. 60, č. 3 (2017), s. 378-395
Number of pages	18 s.
Language	eng - English
Country	US - United States
Keywords	expanders ; pseudorandomness ; communication complexity
Subject RIV	BA - General Mathematics
OECD category	Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
R&D Projects	GBP202/12/G061 GA ČR - Czech Science Foundation (CSF)
Institutional support	MU-W - RVO:67985840
UT WOS	000398890500001
EID SCOPUS	85006124086
DOI	10.1007/s00224-016-9738-5
Annotation	We introduce a new concept, which we call partition expanders. The basic idea is to study quantitative properties of graphs in a slightly different way than it is in the standard definition of expanders. While in the definition of expanders it is required that the number of edges between any pair of sufficiently large sets is close to the expected number, we consider partitions and require this condition only for most of the pairs of blocks. As a result, the blocks can be substantially smaller. We show that for some range of parameters, to be a partition expander a random graph needs exponentially smaller degree than any expander would require in order to achieve similar expanding properties. We apply the concept of partition expanders in communication complexity. First, we construct an optimal pseudo-random generator (PRG) for the Simultaneous Message Passing (SMP) model: it needs n + log k random bits against protocols of cost \Omega(k).
Workplace	Mathematical Institute
Contact	Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757
Year of Publishing	2018

Number of the records: 1