George Danezis and Dahlia Malkhi's article discusses various strategies for transaction execution in DAG-based BFT Consensus protocols, which are crucial for processing transactions at high throughput to match the ordering speeds of modern blockchain systems. The authors explore three main options for transaction execution: post-ordering off-DAG, post-ordering checkpoint on-DAG, and leader-proposed execution, each with its advantages and drawbacks. They also emphasize the importance of parallel execution to accelerate transaction processing, proposing methods such as exploiting transaction concurrency and utilizing concurrency hints for improved performance. Additionally, the article highlights the potential of zk-rollups to offload compute resources from validators and discusses other techniques like dependency graphs and splitting execution to enhance the efficiency of blockchain systems. The discussion reflects ongoing efforts to balance between the network and computational resources to achieve scalable and efficient consensus mechanisms in blockchain technology.