18 research outputs found
Group testing with Random Pools: Phase Transitions and Optimal Strategy
The problem of Group Testing is to identify defective items out of a set of
objects by means of pool queries of the form "Does the pool contain at least a
defective?". The aim is of course to perform detection with the fewest possible
queries, a problem which has relevant practical applications in different
fields including molecular biology and computer science. Here we study GT in
the probabilistic setting focusing on the regime of small defective probability
and large number of objects, and . We construct and
analyze one-stage algorithms for which we establish the occurrence of a
non-detection/detection phase transition resulting in a sharp threshold, , for the number of tests. By optimizing the pool design we construct
algorithms whose detection threshold follows the optimal scaling . Then we consider two-stages algorithms and analyze their
performance for different choices of the first stage pools. In particular, via
a proper random choice of the pools, we construct algorithms which attain the
optimal value (previously determined in Ref. [16]) for the mean number of tests
required for complete detection. We finally discuss the optimal pool design in
the case of finite
Symmetric-key Corruption Detection : When XOR-MACs Meet Combinatorial Group Testing
We study a class of MACs, which we call corruption detectable MAC, that is able to not only check the integrity of the whole message, but also detect a part of the message that is corrupted.
It can be seen as an application of the classical Combinatorial Group Testing (CGT) to message authentication.
However, previous work on this application has inherent limitation in communication.
We present a novel approach to combine CGT and a class of linear MACs (XOR-MAC) that enables to break this limit. Our proposal, XOR-GTM, has a significantly smaller communication cost than any of the previous ones, keeping the same corruption detection capability. Our numerical examples for storage application show a reduction of communication by a factor of around 15 to 70 compared with previous schemes.
XOR-GTM is parallelizable and is as efficient as standard MACs.
We prove that XOR-GTM is provably secure under the standard pseudorandomness assumptions
PCR NONADAPTIVE GROUP TESTING OF DNA LIBRARIES FOR BIOMOLECULAR COMPUTING AND TAGGANT APPLICATIONS
Generalized Framework for Selectors with Applications in Optimal Group Testing
Group Testing refers to the situation in which one is given a set of objects O, an unknown subset P ` O, and the task is to determine P by asking queries of the type "does P intersect Q?", where Q is a subset of O. Group testing is a basic search paradigm that occurs in a variety of situations such as quality control in product testing, searching in storage systems, multiple access communications, and software testing, among the others