带游程限制的拓扑分子存储分组测试
Group Testing with Runlength Constraints for Topological Molecular Storage
摘要：
基于拓扑DNA的数据存储中的应用程序的启发，我们介绍和研究一种新的设置非自适应组测试（NAGT）与游程长度的限制列的测试矩阵，在这个意义上说，任何两个1的必须分开的运行至少D 0的。我们描述和分析的概率构造的游程长度约束的计划中的零误差和消失误差设置，并表明，该建设所需的测试的数量是最佳的对数因子的游程长度约束d和缺陷的数量k在这两种情况下。令人惊讶的是，我们的研究结果表明，游程长度约束NAGT是不是更苛刻的比无约束NAGT时，d=O（k），几乎所有的选择d和k，它是不是更苛刻的比NAGT与列汉明重量约束。为了获得游程长度约束的定量NAGT（QNAGT）计划具有良好的参数，我们还提供了这种设置的下限和一个接近最佳的概率构造QNAGT计划列汉明重量约束。
英文摘要：
Motivated by applications in topological DNA-based data storage, we introduce and study a novel setting of Non-Adaptive Group Testing (NAGT) with runlength constraints on the columns of the test matrix, in the sense that any two 1's must be separated by a run of at least d 0's. We describe and analyze a probabilistic construction of a runlength-constrained scheme in the zero-error and vanishing error settings, and show that the number of tests required by this construction is optimal up to logarithmic factors in the runlength constraint d and the number of defectives k in both cases. Surprisingly, our results show that runlength-constrained NAGT is not more demanding than unconstrained NAGT when d=O(k), and that for almost all choices of d and k it is not more demanding than NAGT with a column Hamming weight constraint only. Towards obtaining runlength-constrained Quantitative NAGT (QNAGT) schemes with good parameters, we also provide lower bounds for this setting and a nearly optimal probabilistic construction of a QNAGT scheme with a column Hamming weight constraint.
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