12 research outputs found

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    LIPIcs, Volume 248, ISAAC 2022, Complete Volume

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    LIPIcs, Volume 248, ISAAC 2022, Complete Volum

    29th International Symposium on Algorithms and Computation: ISAAC 2018, December 16-19, 2018, Jiaoxi, Yilan, Taiwan

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    An asymptotic existence result on compressed sensing matrices

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    For any rational number hh and all sufficiently large nn we give a deterministic construction for an n×⌊hn⌋n\times \lfloor hn\rfloor compressed sensing matrix with (ℓ1,t)(\ell_1,t)-recoverability where t=O(n)t=O(\sqrt{n}). Our method uses pairwise balanced designs and complex Hadamard matrices in the construction of Ï”\epsilon-equiangular frames, which we introduce as a generalisation of equiangular tight frames. The method is general and produces good compressed sensing matrices from any appropriately chosen pairwise balanced design. The (ℓ1,t)(\ell_1,t)-recoverability performance is specified as a simple function of the parameters of the design. To obtain our asymptotic existence result we prove new results on the existence of pairwise balanced designs in which the numbers of blocks of each size are specified.Comment: 15 pages, no figures. Minor improvements and updates in February 201

    Computational Graph Theory

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    Combinatorial designs: a tribute to Haim Hanani

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    Haim Hanani pioneered the techniques for constructing designs and the theory of pairwise balanced designs, leading directly to Wilson''s Existence Theorem. He also led the way in the study of resolvable designs, covering and packing problems, latin squares, 3-designs and other combinatorial configurations.The Hanani volume is a collection of research and survey papers at the forefront of research in combinatorial design theory, including Professor Hanani''s own latest work on Balanced Incomplete Block Designs. Other areas covered include Steiner systems, finite geometries, quasigroups, and t-designs
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