Optimizing Merkle Tree Structure for Blockchain Transactions by a DC Programming Approach

Merkle tree is a fundamental part of blockchain technology, especially in Ethereum cryptocurrency system. The balance of the accounts involved in each transaction is stored on the leaf nodes and must be updated in the State Merkle tree. In this paper, we take advantage of typical transaction characteristics for better constructing the Merkle tree to improve blockchain network performance. It consists of identifying a tree structure with the minimum number of hash values required to update the account data associated with each transaction based on the distribution of all transactions. The proposed optimization model is a combinatorial problem with quadratic functions and binary variables. By using the binary character of variables and penalty techniques, we provide a conventional DC (Difference of Convex functions) program that is efficiently solvable by the DCA (DC Algorithm). Additionally, we suggest an effective recursive DCA-based method for building a Merkle tree for a great amount of blockchain accounts. Numerical experiments on several datasets illustrate the efficiency of our approaches.