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The cluster decay half-lives of heavy nuclei have been calculated within the preformed cluster model by using the microscopic double folding interaction. The densities and the nucleon-nucleon (NN) interactions used are those from relativistic mean field theory. The performance of the relativistic NN interactions with different parametrizations viz. HS, NL2, and NL-SH, together with widely used empirical expressions for the cluster preformation factor are systematically investigated. The NL2 and NL-SH interactions which are especially suitable for describing neutron rich nuclei are found to have better predictive power when combined with an appropriate preformation factor than HS interaction. Predictions of yet to be measured decay half-lives with NL2 interaction together with a proposed empirical expression for the preformation factor are presented. The results are generally seen to compare favourably with the existing theoretical predictions and the available experimental data. [ABSTRACT FROM AUTHOR]