Abstract | ||
---|---|---|
The goal of threshold group testing is to identify up to $d$ defective items among a population of $n$ items, where $d$ is usually much smaller than $n$. A test is positive if it has at least $u$ defective items and negative otherwise. Our objective is to identify defective items sublinear time the number of items, e.g., $mathrm{poly}(d, ln{n}),$ by using the number of tests as low as possible. In this paper, we reduce the number of tests to $O left( h times frac{d^2 ln^2{n}}{mathsf{W}^2(d ln{n})} right)$ and the decoding time to $O left( mathrm{dec}_0 times h right),$ where $mathrm{dec}_0 = O left( frac{d^{3.57} ln^{6.26}{n}}{mathsf{W}^{6.26}(d ln{n})} right) + O left( frac{d^6 ln^4{n}}{mathsf{W}^4(d ln{n})} right)$, $h = Oleft( frac{d_0^2 ln{frac{n}{d_0}}}{(1-p)^2} right)$ , $d_0 = max{u, d - u }$, $p in [0, 1),$ and $mathsf{W}(x) = Theta left( ln{x} - ln{ln{x}} right).$ If the number of tests is increased to $Oleft( h times frac{d^2ln^3{n}}{mathsf{W}^2(d ln{n})} right),$ the decoding complexity is reduced to $O left(mathrm{dec}_1 times h right),$ where $mathrm{dec}_1 = max left{ frac{d^2 ln^3{n}}{mathsf{W}^2(d ln{n})}, frac{ud ln^4{n}}{mathsf{W}^3(d ln{n})} right}.$ Moreover, our proposed scheme is capable of handling errors test outcomes. |
Year | Venue | DocType |
---|---|---|
2019 | arXiv: Information Theory | Journal |
Volume | Citations | PageRank |
abs/1901.02283 | 0 | 0.34 |
References | Authors | |
11 | 4 |
Name | Order | Citations | PageRank |
---|---|---|---|
Thach V. Bui | 1 | 21 | 7.65 |
Minoru Kuribayashi | 2 | 23 | 19.55 |
Mahdi Cheraghchi | 3 | 221 | 21.86 |
Isao Echizen | 4 | 299 | 68.82 |