  The goal of group testing is to efficiently identify a few specific items,
called positives, in a large population of items via tests. A test is an action
on a subset of items which returns positive if the subset contains at least one
positive and negative otherwise. In non-adaptive group testing, all tests are
independent, can be performed in parallel and represented as a measurement
matrix. In this work, we consider non-adaptive group testing with consecutive
positives in which the items are linearly ordered and the positives are
consecutive in that order.
  We proposed two improved algorithms for efficiently identifying consecutive
positives. In particular, without storing measurement matrices, we can identify
up to $d$ consecutive positives with $2 \log_2{\frac{n}{d}} + 2d$ ($4
\log_2{\frac{n}{d}} + 2d$, resp.) tests in $O \left( \log_2^2{\frac{n}{d}} + d
\right)$ ($O \left( \log_2{\frac{n}{d}} + d \right)$, resp.) time. These
results significantly improve the state-of-the-art scheme in which it takes $5
\log_2{\frac{n}{d}} + 2d + 21$ tests to identify the positives in $O \left(
\frac{n}{d} \log_2{\frac{n}{d}} + d^2 \right)$ time with the measurement
matrices associated with the scheme stored somewhere.
