  Digital contact tracing of an infected person, testing the possible infection
for the contacted persons, and isolation play a crucial role in alleviating the
outbreak. Here, we design a dynamic graph streaming algorithm that can trace
the contacts under the control of the Public Health Authorities (PHA). Our
algorithm receives proximity data from the mobile devices as contact data
streams and uses a sliding window model to construct a dynamic contact graph
sketch. Prominently, we introduce the edge label of the contact graph as a
binary contact vector, which acts like a sliding window and holds the latest D
days (incubation period) of temporal social interactions. Notably, the
algorithm prepares the direct and indirect (multilevel) contact list from the
contact graph sketch for a given set of infected persons. Finally, the
algorithm also uses a disjoint set data structure to construct the infection
pathways for the trace list. The present study offers the design of algorithms
with underlying data structures for digital contact trace relevant to the
proximity data produced by Bluetooth enabled mobile devices. Our analysis
reveals that for COVID-19 close contact parameters, the storage space requires
maintaining the contact graph of ten million users; having 14 days of close
contact data in the PHA server takes 55 Gigabytes of memory and preparation of
the contact list for a given set of the infected person depends on the size of
the infected list. Our centralized digital contact tracing framework can also
be applicable for other relevant diseases parameterized by an incubation period
and proximity duration of contacts.

Data Structures and Algorithms;Social and Information Networks