The Internet of Things (IoT) has penetrating all things and objects around us giving them the ability to interact with the Internet, i.e., things become Smart Things (SThs). As a result, SThs produce massive real-time data (i.e., big IoT data). Smartness of IoT applications bases mainly on services such as automatic control, events handling, and decision making. Consumers of the IoT services are not only human users, but also SThs. Consequently, the potential of IoT applications relies on supporting services such as searching, retrieving, mining, analyzing, and sharing real-time data. For enhancing search service in the IoT, our previous work presents a promising solution, called Cluster Representative (ClRe), for indexing similar SThs in IoT applications. ClRe algorithms could reduce similar indexing by O(K − 1), where K is number of Time Series (TS) in a cluster. Multiple extensions for ClRe algorithms were presented in another work for enhancing accuracy of indexed data. In this theme, this paper studies performance analysis of ClRe algorithms, proposes two novel execution methods: (a) Linear execution (LE) and (b) Pair-merge execution (PME), and studies sorting impact on TS execution for enhancing similarity rate for some ClRe extensions. The proposed execution methods are evaluated with real examples and proved using Szeged-weather dataset on ClRe 3.0 and its extensions; where they produce representatives with higher similarities compared to the other extensions. Evaluation results indicate that PME could improve performance of ClRe 3.0 by = 20.5%, ClRe 3.1 by = 17.7%, and ClRe 3.2 by = 6.4% in average.