  In this work, we are concerned with maximizing the lifetime of a cluster of
sensors engaged in single-hop communication with a base-station. In a
data-gathering network, the spatio-temporal correlation in sensor data induces
data-redundancy. Also, the interaction between two communicating parties is
well-known to reduce the communication complexity. This paper proposes a
formalism that exploits these two opportunities to reduce the number of bits
transmitted by a sensor node in a cluster, hence enhancing its lifetime. We
argue that our approach has several inherent advantages in scenarios where the
sensor nodes are acutely energy and computing-power constrained, but the
base-station is not so. This provides us an opportunity to develop
communication protocols, where most of the computing and communication is done
by the base-station.
  The proposed framework casts the sensor nodes and base-station communication
problem as the problem of multiple informants with correlated information
communicating with a recipient and attempts to extend extant work on
interactive communication between an informant-recipient pair to such
scenarios. Our work makes four major contributions. Firstly, we explicitly show
that in such scenarios interaction can help in reducing the communication
complexity. Secondly, we show that the order in which the informants
communicate with the recipient may determine the communication complexity.
Thirdly, we provide the framework to compute the $m$-message communication
complexity in such scenarios. Lastly, we prove that in a typical sensor network
scenario, the proposed formalism significantly reduces the communication and
computational complexities.
