Recent advances in low power radios and sensor technology have enabled the pervasive deployment of sensor networks consisting of sensor nodes that are very small in size and relatively inexpensive. Wireless Sensor Networks (WSNs) have been seen more as a solution to large scale tracking and monitoring applications, because their low data rate, low energy consumption and short range communication presents the great opportunity to instrument and monitor the physical world at unprecedented scale.

However realization of WSNs needs to satisfy constraints introduced by factors such as limited power, limited communication bandwidth, limited processing capacity, and small storage capacity. Therefore, the design of efficient technique for optimizing the capabilities of networks is becoming an increasingly critical aspect in networking. This paper addresses constrained optimization problems namely the Capacitated Minimum Forest (CMF) problem. To utilize the critical WSNs resources precisely, the development of algorithms with quality guaranteed solutions in WSNs is needed. We proposed that optimal approximation algorithms achieve highest optimization goal which minimize Cost of network resource consumption.

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