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• W3100593671 abstract "An $$mtimes n$$ matrix $$mathsf {A}$$ with column supports $${S_i}$$ is k-separable if the disjunctions $$bigcup _{i in mathcal {K}} S_i$$ are all distinct over all sets $$mathcal {K}$$ of cardinality k. While a simple counting bound shows that $$m > k log _2 n/k$$ rows are required for a separable matrix to exist, in fact it is necessary for m to be about a factor of k more than this. In this paper, we consider a weaker definition of ‘almost k-separability’, which requires that the disjunctions are ‘mostly distinct’. We show using a random construction that these matrices exist with $$m = O(k log n)$$ rows, which is optimal for $$k = O(n^{1-beta })$$ . Further, by calculating explicit constants, we show how almost separable matrices give new bounds on the rate of nonadaptive group testing." @default.
• W3100593671 created "2020-11-23" @default.
• W3100593671 creator A5021110395 @default.
• W3100593671 creator A5022492185 @default.
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• W3100593671 date "2015-10-12" @default.
• W3100593671 modified "2023-09-24" @default.
• W3100593671 title "Almost separable matrices" @default.
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• W3100593671 doi "https://doi.org/10.1007/s10878-015-9951-1" @default.
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