Analysis of Variance of Graph-Clique Mining for Scalable Proof of Work

Recently, Bitcoin is becoming one of the most popular decentralized cryptographic currency technologies, and Bitcoin mining is a process of adding transaction records to Bitcoin’s public ledger of past transactions or blockchain. To obtain a bitcoin, the mining process involves compiling recent transactions into blocks and trying to solve a computationally difficult puzzle, e.g., proof of work puzzle. A proof of work allows miners the ability to quantify how much work a given proof contains. Basically, the required time for mining is decided in advance, but problems will occur if the value is large for dispersion. In this paper, we first accept that the required time between consecutive blocks follows the exponential distribution. That is, the variance is stable as long as the expected time is fixed. Then, we focus on the graph clique mining technique proposed by the literature, like Tromp (BITCOIN 2015) and Bag-Ruj-Sakurai (Inscrypt 2015), which is based on a computational difficulty problem of searching cliques of undirected graphs, where a clique is a subset of vertices. In particular, when the clique size is two, graph clique mining can be used to gain Bitcoins. The previous work also claimed that if the clique size is parameterized and increased, even if the expected time is fixed, the variance would not be stable. However, no qualitative or quantitative results were given to support their claim. Motivated by this issue, in this work, we propose a simple search algorithm for graph cliques mining, and perform a small scale evaluation on Bitcoin and Graph cliques’s solo mining to investigate the variance issue.