Reconstruction of time-varying gene regulatory networks underlying a time-series gene expression data is a fundamental challenge in the computational systems biology. The challenge increases multi-fold if the target networks need to be constructed for hundreds to thousands of genes. There have been constant efforts to design an algorithm that can perform the reconstruction task correctly as well as can scale efficiently (with respect to both time and memory) to such a large number of genes. However, the existing algorithms either do not offer time-efficiency, or they offer it at other costs - memory-inefficiency or imposition of a constraint, known as the 'smoothly time-varying assumption'. In this article, two novel algorithms - 'an algorithm for reconstructing Time-varying Gene regulatory networks with Shortlisted candidate regulators - which is Light on memory' (TGS-Lite) and 'TGS-Lite Plus' (TGS-Lite+) - are proposed that are time-efficient, memory-efficient and do not impose the smoothly time-varying assumption. Additionally, they offer state-of-the-art reconstruction correctness as demonstrated with three benchmark datasets. Source Code: https://github.com/sap01/TGS-Lite-supplem/tree/master/sourcecode. © 2004-2012 IEEE.