Publication Date: 2025
Journal of Combinatorial Optimization (13826905)49(1)
In this work, we consider a combinatorial optimization problem with direct applications in blockchain mining, namely finding the most lucrative blocks for Bitcoin miners, and propose optimal algorithmic solutions. Our experiments show that our algorithms increase the miners’ revenues by more than a million dollars per month. Modern blockchains reward their miners in two ways: (i) a base reward for each block that is mined, and (ii) the transaction fees of those transactions that are included in the mined block. The base reward is fixed by the respective blockchain’s protocol and is not under the miner’s control. Hence, for a miner who wishes to maximize earnings, the fundamental problem is to form a valid block with maximal total transaction fees and then try to mine it. Moreover, in many protocols, including Bitcoin itself, the base reward halves at predetermined intervals, hence increasing the importance of maximizing transaction fees and mining an optimal block. This problem is further complicated by the fact that transactions can be prerequisites of each other or have conflicts (in case of double-spending). In this work, we consider the problem of forming an optimal block, i.e. a valid block with maximal total transaction fees, given a set of unmined transactions. On the theoretical side, we first formally model our problem as an extension of Knapsack and then show that, unlike classical Knapsack, our problem is strongly NP-hard. We also show a hardness-of-approximation result. As such, there is no hope in solving it efficiently for general instances. However, we observe that its real-world instances are quite sparse, i.e. the transactions have very few dependencies and conflicts. Using this fact, and exploiting three well-known graph sparsity parameters, namely treedepth, treewidth and pathwidth, we present exact linear-time parameterized algorithms that are applicable to the real-world instances and obtain optimal results. On the practical side, we provide an extensive experimental evaluation demonstrating that our approach vastly outperforms the current Bitcoin miners in practice, obtaining a significant per-block average increase of 11.34 percent in transaction fee revenues which amounts to almost one million dollars per month. © The Author(s) 2024.
