In this paper we consider three distributed decision making tasks that arise in the design and configuration of multi-hop wireless networks: medium access scheduling, Hamiltonian cycle formation, and the partitioning of network nodes into coordinating cliques. We first model these tasks as distributed constraint satisfaction problems (DC-SPs). We first show that the communication complexity of DCSPs can be related to the computational complexity of centralized constraint satisfaction problems. We then use centralized algorithms to obtain experimental results on the solvability and complexity of the three DCSPs. We show that these problems exhibit “phase transitions ” in solvability and complexity as the transmission power of the wireless nodes is varied. Based on these results, we argue that phase transition analysis provides a mechanism for quantifying the critical range of network resources needed for scalable, self-configuring multi-hop wireless networks.
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