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Top1. Introduction
With the recent technological advances, the amount of data being collected and stored is increasing at an exponential rate. The challenges and problems faced by applications involving the use of big datasets have been listed in Hassanien et al (2015). To analyse and extract valuable information out of the big data, data mining techniques are applied on such passive data, most of which is modelled in the form of a dynamic network consisting of sequence of graphs being evolved over time. A considerable amount of effort has been put in to study the evolution of interactions in a dynamic network (Apostolico et al., 2011; Borgwardt et al., 2006; Desikan & Srivastava, 2006; Duan et al., 2009; Gupta et al., 2014; Halder et al., 2013; Inokuchi et al., 2000; Lahiri & Wolf, 2010; Liu et al., 2009; Obulesu et al., 2014; Qin et al., 2011; Rasheed et al., 2011; Yang et al., 2014). Among these, a good amount of emphasis has been laid on interactions that exhibit frequent behaviour (Borgwardt et al., 2006; Inokuchi et al., 2000; Yang et al., 2014). Also, a substantial effort has been put in to study regular behaviour of interactions (Gupta et al., 2014; Qin et al., 2011).
However, an interaction tends to exhibit other important occurrence patterns, such as periodic patterns which repeat after a fixed interval of time. The first step to study periodic behaviour has been marked through the development of a model based on similarity of time sequences used for mining periodic patterns (Srikant & Agrawal, 1996). Afterwards, Ozden et al. (1998) have constructed a model for discovery of association rules displaying regular cyclic variation over time. It has been followed by construction of a model (Han et al., 1999) for efficient mining of partial periodic patterns in a time series database. Later, an algorithm (Ma & Hellerstein, 2001) has been proposed for mining partially periodic event patterns with unknown periods. Subsequently, Berberidis et al. (2002) have proposed an approach to deal with datasets in which periodicity is not known in advance. Further, a model (Yang, 2003) has been introduced to mine asynchronous periodic patterns. Later, Lahiri & Wolf (2010) have proposed an algorithm to mine parsimonious periodic patterns on a dynamic network. Subsequently, an improvement (Apostolico et al., 2011) of the algorithm (Lahiri & Wolf, 2010) in terms of time complexity has been proposed and a noise resilient suffix tree based approach (Rasheed et al., 2011) has been provided to detect all periodic patterns in a time series and sequence database. Later, a new approach (Halder et al., 2013) has been given based on super graph for discovering periodic patterns. Further, a framework (Obulesu et al., 2014) has been proposed to find frequent and maximal periodic patterns in Spatiotemporal Databases having big data.