Time-efficient algorithms for the outdegree limited bluetooth scatternet formation problem

We present in this paper three Bluetooth Scatternet Formation (BSF) algorithms which forms deterministically connected and outdegree limited scatternets. Our algorithms improve the execution time of algorithm BlueMIS, which consists of two consecutive phases called BlueMIS I and BlueMIS II. The first phase, BlueMIS I, is a BSF algorithm that forms connected and outdegree limited scatternets in a time-efficient manner. Our algorithms improve BlueMIS by improving BlueMIS I. First, we introduce a time-efficient implementation of communication rounds, called OrderedExchange, that is more suitable for Bluetooth networks, where in a communication round each node sends and receives a message to and from all its neighbors. Using OrderedExchange, we introduce algorithms ComputeMIS I and ComputeMIS II which form the same scatternet as those formed by BlueMIS I but with less execution time. We also introduce algorithm Eliminate. Instead of letting each node u forms a maximal independent set of all its neighbors and then considers them as slaves, as in the case of BlueMIS I, Eliminate let each node u forms a maximal independent set of all its neighbors that have smaller identifiers. Eliminate forms scatternets that are similiar to those formed by BlueMIS I, and more efficient with respect to some performance metrics. Eliminate improves the execution time of ComputeMIS I and ComputeMIS II by about 60%.