3 research outputs found
On a Hypergraph Approach to Multistage Group Testing Problems
Group testing is a well known search problem that consists in detecting up to
defective elements of the set by carrying out tests on
properly chosen subsets of . In classical group testing the goal is to
find all defective elements by using the minimal possible number of tests. In
this paper we consider multistage group testing. We propose a general idea how
to use a hypergraph approach to searching defects. For the case , we
design an explicit construction, which makes use of tests in
the worst case and consists of stages.Comment: ACCT 2016, 6 page
A New Algorithm for Two-Stage Group Testing
Group testing is a well-known search problem that consists in detecting of
defective members of a set of samples by carrying out tests on properly
chosen subsets of samples. In classical group testing the goal is to find all
defective elements by using the minimal possible number of tests in the worst
case. In this work, two-stage group testing is considered. Using the hypergraph
approach we design a new search algorithm, which allows improving the known
results for fixed and . For the case this algorithm
achieves information-theoretic lower bound on the number of
tests in the worst case. Also, the problem of finding out of defectives
is considered.Comment: 7 pages, 1 tabl
Optimal Multistage Group Testing Algorithm for 3 Defectives
Group testing is a well-known search problem that consists in detecting of
defective members of a set of samples by carrying out tests on properly
chosen subsets of samples. In classical group testing the goal is to find all
defective elements by using the minimal possible number of tests in the worst
case. In this work, a multistage group testing problem is considered. Our goal
is to construct a multistage search procedure, having asymptotically the same
number of tests as the optimal adaptive algorithm. We propose a new approach to
designing multistage algorithms, which allows us to construct a 5-stage
algorithm for finding 3 defectives with the optimal number
of tests