Ethereum, as a representative of Web3, adopts a novel framework called Proposer Builder Separation (PBS) to prevent the centralization of block profits in the hands of institutional Ethereum stakers. Introducing builders to generate blocks based on public transactions, PBS aims to ensure that block profits are distributed among all stakers. Through the auction among builders, only one will win the block in each slot. Ideally, the equilibrium strategy of builders under public information would lead them to bid all block profits. However, builders are now capable of extracting profits from private order flows. In this paper, we explore the effect of PBS with private order flows. Specifically, we propose the asymmetry auction model of MEV-Boost auction. Moreover, we conduct empirical study on Ethereum blocks from January 2023 to May 2024. Our analysis indicates that private order flows contribute to 54.59% of the block value, indicating that different builders will build blocks with different valuations. Interestingly, we find that builders with more private order flows (i.e., higher block valuations) are more likely to win the block, while retain larger proportion of profits. In return, such builders will further attract more private order flows, resulting in a monopolistic market gradually. Our findings reveal that PBS in current stage is unable to balance the profit distribution, which just transits the centralization of block profits from institutional stakers to the monopolistic builder.

To measure repair latency at helper nodes, we introduce a new metric called skip cost that quantifies the number of contiguous sections accessed on a disk. We provide explicit constructions of zigzag codes and fractional repetition codes that incur zero skip cost.

Gradient coding is a distributed computing technique aiming to provide robustness against slow or non-responsive computing nodes, known as stragglers, while balancing the computational load for responsive computing nodes. Among existing gradient codes, a construction based on combinatorial designs, called BIBD gradient code, achieves the best trade-off between robustness and computational load in the worst-case adversarial straggler setting. However, the range of system parameters for which BIBD gradient codes exist is limited. In this paper, we overcome this limitation and propose a new probabilistic gradient code, termed Sparse Gaussian (SG) gradient code. The encoding matrix of the proposed SG gradient code is generated from a carefully chosen correlated multivariate Gaussian distribution, masked by Bernoulli random variables to reduce computational load. With high probability, the proposed gradient code achieves a similar worst-case error performance compared to the BIBD gradient code (when such a code of the same parameters exists) and outperforms several other existing gradient codes, including Fractional Repetition gradient codes and Bernoulli gradient codes. Moreover, it further extends the range of system parameters over existing BIBD and soft BIBD gradient codes, making it a promising solution for distributed computing tasks.