Forming MS-Free and Outdegree-Limited Bluetooth Scatternets in Pessimistic Environments

This paper introduces two distributed Bluetooth scatternet formation (BSF) algorithms, called BSFWAVVY(MSF) and 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 outdegreelimited scatternets at the same time is NP-COMPLETE. We introduce a time-efficient implementation of BSFWAVVY(MSF) and 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.