348,359 research outputs found
Constraining the Number of Positive Responses in Adaptive, Non-Adaptive, and Two-Stage Group Testing
Group testing is a well known search problem that consists in detecting the
defective members of a set of objects O by performing tests on properly chosen
subsets (pools) of the given set O. In classical group testing the goal is to
find all defectives by using as few tests as possible. We consider a variant of
classical group testing in which one is concerned not only with minimizing the
total number of tests but aims also at reducing the number of tests involving
defective elements. The rationale behind this search model is that in many
practical applications the devices used for the tests are subject to
deterioration due to exposure to or interaction with the defective elements. In
this paper we consider adaptive, non-adaptive and two-stage group testing. For
all three considered scenarios, we derive upper and lower bounds on the number
of "yes" responses that must be admitted by any strategy performing at most a
certain number t of tests. In particular, for the adaptive case we provide an
algorithm that uses a number of "yes" responses that exceeds the given lower
bound by a small constant. Interestingly, this bound can be asymptotically
attained also by our two-stage algorithm, which is a phenomenon analogous to
the one occurring in classical group testing. For the non-adaptive scenario we
give almost matching upper and lower bounds on the number of "yes" responses.
In particular, we give two constructions both achieving the same asymptotic
bound. An interesting feature of one of these constructions is that it is an
explicit construction. The bounds for the non-adaptive and the two-stage cases
follow from the bounds on the optimal sizes of new variants of d-cover free
families and (p,d)-cover free families introduced in this paper, which we
believe may be of interest also in other contexts
Efficient Two-Stage Group Testing Algorithms for Genetic Screening
Efficient two-stage group testing algorithms that are particularly suited for
rapid and less-expensive DNA library screening and other large scale biological
group testing efforts are investigated in this paper. The main focus is on
novel combinatorial constructions in order to minimize the number of individual
tests at the second stage of a two-stage disjunctive testing procedure.
Building on recent work by Levenshtein (2003) and Tonchev (2008), several new
infinite classes of such combinatorial designs are presented.Comment: 14 pages; to appear in "Algorithmica". Part of this work has been
presented at the ICALP 2011 Group Testing Workshop; arXiv:1106.368
Revisiting nested group testing procedures: new results, comparisons, and robustness
Group testing has its origin in the identification of syphilis in the US army
during World War II. Much of the theoretical framework of group testing was
developed starting in the late 1950s, with continued work into the 1990s.
Recently, with the advent of new laboratory and genetic technologies, there has
been an increasing interest in group testing designs for cost saving purposes.
In this paper, we compare different nested designs, including Dorfman, Sterrett
and an optimal nested procedure obtained through dynamic programming. To
elucidate these comparisons, we develop closed-form expressions for the optimal
Sterrett procedure and provide a concise review of the prior literature for
other commonly used procedures. We consider designs where the prevalence of
disease is known as well as investigate the robustness of these procedures when
it is incorrectly assumed. This article provides a technical presentation that
will be of interest to researchers as well as from a pedagogical perspective.
Supplementary material for this article is available online.Comment: Submitted for publication on May 3, 2016. Revised versio
- …