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Top1. Introduction
In recent years, peer-to-peer (P2P) systems have attracted plenty of interests in many communities because of their inherent potentials such as high scalability, fault tolerance, and cost-effectiveness (Gupta and Awasthi, 2010; Gao et al., 2013; Surati et al., 2015; Chen et al., 2016). An important application of the P2P paradigm is distributed storage, where data files are stored with proper redundancy at different nodes which allows efficient retrieval and low probability of error (Meng and Li, 2013; Han et al., 2014; Amoretti and Zanichelli, 2016; Sun et al., 2019). In a P2P-based system, users place their data on storage nodes using proper encoding functions, thus generating redundancy to counter-act possible faults. To improve data availability, P2P-based storage systems generally rely on multiple unreliable nodes to accommodate data replicas. In this way, the replicated data can be retrieved from any of these nodes and therefore a P2P system allows participated peers leaving/joining the system in a flexible manner (Jiang et al., 2014; Martalo et al., 2014; Yao et al., 2015; Shojafar et al., 2017; Feng et al., 2019). Such a feature makes P2P storage systems being popular in many communities, such as volunteering computing and distributed stream video applications (Rosas et al., 2014; Susilo et al., 2015; Lucchese, 2018; Khang et al., 2019).
On the other side, multiple replicas coexisting in a distributed platform makes the data consistency service being necessary, otherwise data-updating operation in one replica may lead to data inconsistency in other peers (Li et al., 2008; Xu et al., 2010; Meng, 2018). Consistency maintenance mechanism is necessary for P2P applications due to their frequent data-updating operations. Although many previous studies have addressed the issue of data updating problem (Tamura et al., 2008; Shen, 2010; Garcia-Garcia et al., 2013; Han et al., 2014; Yao et al., 2015; Shojafar et al., 2017; Wang, 2018), few of them are able to provide strict consistency in real-world scenarios, where data items may be buffered or replicated in multiple storage nodes. Meanwhile, the centralized approaches often suffer from single point of failures, while previous decentralized approaches consume too many network resources because of locality-ignorant structures. For instance, some of these approaches are based on the single-writer strategy, while some others require specific structural features for managing data replicas. Unfortunately, none of them can effectively deal with the problem of maintaining strong consistency among multiple storage nodes in a highly dynamic setting. It is noteworthy that the recent mentioned quorums strategy (Abawajy and Deris, 2014; Kong et al., 2014; Susilo et al., 2015; Poenaru et al., 2018) can deal with the data consistency problem, however, it may introduce extra communication overheads due to the consensus requirement in each progress step (Wang et al., 2011; Hu et al., 2012; Xu et al., 2015; Zhang et al., 2018).
Motivated by the above observations, we design a novel data-updating model, virtual peers based data consistency (VPDC), which introduces a set of virtual peers to provide guaranteed data consistency in decentralized and unstructured P2P systems. The proposed VPDC model can be easily implemented in any current P2P storage systems without interfering the functions of data retrieving, and also it is incorporated with several mechanisms to ensure the reliability during the runtime. The main contributions of this study are summarized as following: