Top rollups scaling solution comparison

Optimism
Optimism pioneered the implementation of Optimistic Rollups in 2019 using the Optimism Virtual Machine (OVM), which was compatible with the Ethereum Virtual Machine (EVM). This compatibility required additional work for every application to function on Optimism, including even simple ones like Uniswap, which needed custom code. However, the Optimism team realized that this approach wasn't ideal for Ethereum's rapidly growing ecosystem. They decided to transition the OVM into an environment equivalent to the EVM to leverage the mature infrastructure already available for Ethereum. This change ensured that applications and software could seamlessly operate on Optimism, aligning with Ethereum's Yellow Paper standard. To achieve this, the Optimism team minimized their codebase and utilized Geth, the official Go implementation of the EVM, for their client, prioritizing simplicity as a core value.
Users interact with a sequencer on layer two, responsible for aggregating and executing transactions and creating rollups to transmit data to layer one. If a fraudulent rollup is detected, a verifier submits a fault proof for a single transaction in the batch, handled by the rollup smart contract. This process, while simple, requires layer one to compute entire transactions, ranging from token transfers to complex smart contract executions, placing the computational burden on the Ethereum chain during disputes.

Optimism aims for further advancements, especially in decentralizing the sequencer node, which currently operates solely by Optimism, posing a risk to censorship resistance. To address this, the Optimism team proposed implementing a Miner Extractable Value (MEV) Auction, separating transaction inclusion and ordering to solve the MEV problem. Additionally, they organized a contest with Synthetix to test rollups' capabilities, showcasing high performance and significantly lower fees compared to Ethereum under normal conditions.

Arbitrum
Arbitrum, developed by Offchain Labs since 2018, is a second-layer network utilizing optimistic rollups. Unlike Optimism, Arbitrum focuses on minimizing Ethereum network computations during dispute resolutions, albeit at the expense of simplicity. When a verifier node, known as a validator in Arbitrum, submits a fault proof for a rollup, it initiates a dispute period alongside the aggregator using a K-way Dissection protocol, although here we simplify it to a Bisection version.

During the Arbitrum Challenge Period setup, assuming a large amount of Ether (B), two players—aggregator Alice and validator Bob—are involved. Alice submits a rollup with transactions representing instructions to L1 alongside a bond (B). If Bob disagrees and submits a fault proof, staking a bond as well, they enter the Challenge period. This period includes a dissection phase to find conflicting instructions and a one-step proof phase to prove validity or failure to layer one.

The Arbitrum Virtual Machine (AVM) is designed to minimize data disclosure when submitting a one-step proof. It uses an approach similar to lazy lists, obfuscating the data until necessary for proof. This design ensures correctness, efficiency, and pseudo-privacy, resolving disputes in logarithmic time and hiding most AVM workings for privacy.

On the technical side, Arbitrum aims for high TPS and fee reductions compared to layer one but is currently throttled, gradually scaling to its full potential. Anytrust, released in early 2022, offers even higher TPS and lower fees, working alongside Arbitrum's rollup.
Like Optimism, Offchain Labs operates the sole Sequencer on Arbitrum but plans to implement a Decentralized Fair Sequencing algorithm for fair transaction ordering through a committee of servers. However, ensuring a fair ordering requires a super-majority of non-malicious servers.