Algorithms for capacitated minimum spanning tree problem

The devices, which are running on Wireless Sensor Networks (WSNs), generally have limited energy sources. Thus, makes foregrounding the design of "Energy-Aware" types of algorithms. Capacitated Minimum Spanning Tree (CMST) algorithms can be designed for finding energy-aware routing paths and for load-balancing among sub-trees connected to the sink device. Although, there are studies extensively in central settings there has not been any energy-efficient algorithm for the WSNs. The bit complexity of applying a central approach in the sink node is O(n^2 log⁡n) bits on a network having n nodes. In this study, we present the design of algorithms which aim to solve CMST problem in WSNs. DCMST is based on DIST_PRIM (DPRIM) algorithm and MCO is based on Esau-Williams (E-W) algorithm. The bit complexity of the proposed DCMST algorithm is O(n^2) bits and identical with DIST_PRIM. The bit complexity of the proposed MCO algorithm is O(n log⁡n) bits. We compare the performance of the proposed DCMST algorithm with DPRIM and central version of DCMST algorithm (CENTRAL). The performance of the proposed MCO algorithm with the straightforward implementation of E-W, where the problem is solved by the sink node and the result is sent to the other nodes (CENTEW) on WSN. According to the computational results, DPRIM and MCO algorithms are more efficient than CENTRAL and CENTEW algorithms with respect to the energy consumption.