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JOURNAL OF COMPUTATIONAL BIOLOGY
Volume 10, Number 2, 2003
© Mary Ann Liebert, Inc.
Pp. 231–236
ErrorTolerant Pooling Designs with Inhibitors
F.K. HWANG and Y.C. LIU
ABSTRACT
Pooling designs are used in clone library screening to efŽ ciently distinguish positive clones
from negative clones. Mathematically, a pooling design is just a nonadaptive group testing
scheme which has been extensively studied in the literature. In some applications, there is a
third category of clones called “inhibitors” whose effect is to neutralize positives. SpeciŽ cally,
the presence of an inhibitor in a pool dictates a negative outcome even though positives are
present. Sequential group testing schemes, which can be modiŽ ed to threestage schemes,
have been proposed for the inhibitor model, but it is unknown whether a pooling design
(a onestage scheme) exists. Another open question raised in the literature is whether the
inhibitor model can treat unreliable pool outcomes. In this paper, we answer both open prob
lems by giving a pooling design, as well as a twostage scheme, for the inhibitor model with
unreliable outcomes. The number of pools required by our schemes are quite comparable
to the threestage scheme.
Key words:
nonadaptive group testing, inhibitors, errortolerant.
1. INTRODUCTION
S
equencing a set of clones often relies
on identifying the clones which contain a given probe. For
examples, in physical mapping, the probe can be a sequencetagged site which is a unique subsequence
in the target sequence. The identiŽ cation of a clone containing this probe essentially locates the clone. In
a DNA array, a probe is a given
l
tuple and a positive identiŽ cation conŽ rms the existence of such an
l
tuple in the target sequence. We will assume that the setting is in the Ž rst application, namely, to identify
which clones in the given set contain the probe. A clone is called a
positive
if it contains the probe, and a
negative
if not. A
pool
is a subset of clones put together for a joint assay with two possible outcomes: a
negative pool
signiŽ es that there’s no positive in the pool, a
positive pool
signiŽ es otherwise, namely, that
there is at least one positive in the pool. A
pooling design
is a 01 matrix where the columns are the set
of clones, the rows are the set of pools, and a 1entry in cell
.i; j/
signiŽ es that clone
j
is in pool
i
.
In some biological applications, there is a third category of clones called
inhibitors
whose presence
in a pool dictates a negative outcome, regardless of the presence of a positive in the pool. While the
pooling design corresponds to the classical nonadaptive group testing problem (Du and Hwang, 2000), the
presence of inhibitors presents a new group testing model not considered in the group testing literature.
Farach
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 Spring '08
 UNGOR

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