This paper introduces two distributed Bluetooth scatternet formation (BSF) algorithms, called $\mathtt{BSFWAVVY(MSF)}$ and $\mathtt{BSFWAVVY(ODL)}$ . The first algorithm forms scatternets that does not contain master–slave (MS) bridges (MS-free scatternets), whereas the second algorithm forms scatternets in which each piconet has at most $k$ slaves (outdegree-limited scatternets). The motivation is that MS-freeness and outdegree limitation are the two properties that significantly improve the quality of the scatternets. However, and contrary to the existing BSF algorithms, our algorithms consider these properties under pessimistic environments modeled as arbitrary networks (i.e., no assumptions are made on the underlying network topology). We give two lower bounds that prove the asymptotic optimality of our algorithms with respect to time complexity and message complexity. We also show that the problem of forming MS-free and outdegree-limited scatternets at the same time is ${\sf{NP}}$ - ${\sf{COMPLETE}}$ . We introduce a time-efficient implementation of $\mathtt{BSFWAVVY(MSF)}$ and $\mathtt{BSFWAVVY(ODL)}$ that exploits unique characteristics of Bluetooth networks. Simulation experiments show that our algorithms have short execution time relative to major BSF algorithms and it outperforms other major algorithms with respect to various performance metrics.
Read full abstract