Network-wide broadcast (simply broadcast) is a frequent operation in wireless ad hoc net-
works. A simple °ooding based implementation of broadcast may result in excessive use
of system energy and wireless bandwidth that are two scarce resources in wireless ad hoc
networks. One promising practical approach to improve the e±ciency of broadcast is to
use localized algorithms that minimize the number of nodes involved in the propagation of
broadcast messages. In this context, the minimum forwarding set problem (MFSP) (also
known as multi-point relay (MPR) selection problem) has received a considerable attention
in the research community. Even though the general form of the problem is shown to be NP-
complete, the complexity of the problem has not been known under the practical application
context of ad hoc networks.
In this study, I present two polynomial time algorithms to solve the MFSP for wireless
networks under unit disk coverage model and disk coverage model. Leveraging the practical
characteristics of the application environment, I prove the existence of a certain class of
optimal solutions that hold some nice properties. I then propose polynomial time algorithms
to build an optimal solution within this class of solutions to a given instance of the MFSP
problem. My algorithms are the ¯rst polynomial time solutions to the MFSP problem under
these models.
Furthermore I present a new version of MFSP which provides collision awareness. I believe
that the work presented in this thesis will have an impact on the design and development of
new algorithms for several wireless network applications including energy e±cient multicast
and broadcast protocols; energy e±cient topology control protocols; and energy e±cient
virtual backbone construction protocols for wireless ad hoc networks and sensor networks. |