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Wavelength conversion and routing are the two key techniques used for improvement of the overall blocking performance in wavelength routed all-optical networks. As wavelength converters are very expensive, the effective use of wavelength converters or more precisely placement of minimum number of wavelength converter in the appropriate nodes in the network is a challenging issue in the field of wavelength division multiplexing (WDM) optical networks. In this paper, we have studied the performance of sparse complete wavelength conversion (SCWC) network architecture. An efficient heuristic-based algorithm is proposed based on alternate routing minimum blocking probability (ARMBP) for efficient placement of wavelength converters under K-alternate routing with shortest path first-first fit (AR-SPF-FF) routing and wavelength assignment. The performance of our proposed algorithm is analyzed with the help of extensive simulations for a wide range of network topology. The results show that our proposed approach produces better performance compared to the existing wavelength converter placement algorithms.