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Partition expanders

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    0473687 - MÚ 2018 RIV US eng J - Journal Article
    Gavinsky, Dmitry - Pudlák, Pavel
    Partition expanders.
    Theory of Computing Systems. Roč. 60, č. 3 (2017), s. 378-395. ISSN 1432-4350
    R&D Projects: GA ČR GBP202/12/G061
    Institutional support: RVO:67985840
    Keywords : expanders * pseudorandomness * communication complexity
    Subject RIV: BA - General Mathematics
    OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
    Impact factor: 0.458, year: 2017
    http://link.springer.com/article/10.1007%2Fs00224-016-9738-5

    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).
    Permanent Link: http://hdl.handle.net/11104/0270815
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