  The group testing approach that achieves significant cost reduction over the
individual testing approach has received a lot of interest lately for massive
testing of COVID-19. Many studies simply assume samples mixed in a group are
independent. However, this assumption may not be reasonable for a contagious
disease like COVID-19. Specifically, people within a family tend to infect each
other and thus are likely to be positively correlated. By exploiting positive
correlation, we make the following two main contributions. One is to provide a
rigorous proof that further cost reduction can be achieved by using the Dorfman
two-stage method when samples within a group are positively correlated. The
other is to propose a hierarchical agglomerative algorithm for pooled testing
with a social graph, where an edge in the social graph connects frequent social
contacts between two persons. Such an algorithm leads to notable cost reduction
(roughly 20%-35%) compared to random pooling when the Dorfman two-stage
algorithm is applied.
