Este artigo analisa estratégias de otimização de gas em Ethereum a partir de duas dimensões principais: o custo dos opcodes da EVM e as escolhas de estruturas de dados em Solidity. A tabela de opcodes da EVM e a evolução do gas schedule mostram que operações de armazenamento e acesso externo, como SSTORE, SLOAD, CALL, BALANCE e EXT*, estão entre as mais caras, especialmente após EIPs como a 2929, que aumentaram o custo de acessos “frios” a contas e slots de storage para refletir melhor seu impacto na execução e na camada de armazenamento. Estudos recentes sobre custos de armazenamento evidenciam que uma escrita em SSTORE pode custar cerca de 22.100 gas para 32 bytes (aprox. 690 gas/byte), enquanto leituras via SLOAD também são significativamente caras, motivando pesquisas sobre técnicas como SSTORE2 e mecanismos para corrigir “overcharge” em leitura/escrita de storage, com ganhos médios de até 30–32% em fees para certos padrões de uso. Boas práticas de otimização de gas em Solidity incluem reduzir o número de acessos a storage movendo valores frequentemente lidos para variáveis em memória, empacotar variáveis em slots de 32 bytes (storage packing), preferir tipos fixos a dinâmicos quando possível, evitar cópias desnecessárias de arrays de storage para memória e desenhar estruturas de dados que minimizem gravações em storage. A literatura e guias de otimização indicam que a escolha entre arrays, mappings, structs e padrões de layout impacta diretamente o custo de execução, especialmente em loops que interagem com storage ou estruturas dinâmicas. Conclui‑se que a otimização de gas em Ethereum é um problema tanto de engenharia de baixo nível, ligado ao custo de opcodes e ao modelo warm/cold de acessos, quanto de design de dados e algoritmos, com implicações econômicas diretas para usuários, protocolos DeFi e estratégias de design de L2s.<br>
Stochastic Bit-Parallel Maximum Clique Solver (1024-bit Virtual Register) We introduce a stochastic bit-parallel solver for the Maximum Clique Problem (MCP) based on a 1024-bit virtual register architecture implemented as 16 contiguous uint64_t words in standard C++17, ensuring full portability across 64-bit platforms (x86-64, ARM, RISC-V). Core operations—candidate intersection, population count, and leading-zero detection—execute in exactly 16 instructions per 1024-bit operation. The solver integrates three key components: (i) a co-neighborhood heuristic that identifies high-coreness nodes via O(N²) pairwise popcount over 1024-bit adjacency rows; (ii) a stochastic swarm of independent worker threads; and (iii) greedy clique expansion through iterative bitwise intersection. Exact branch-and-bound solvers (MaxCliqueDyn, MCQ) become computationally intractable on dense random graphs such as G(1024, 0.5), where chromatic coloring bounds lose effectiveness and the search tree grows exponentially, requiring hours of computation on commodity hardware. The proposed method operates specifically within this hard regime, achieving 100% recovery of all 28 planted clique vertices in 153 milliseconds—a setting where exact state-of-the-art methods cannot remain competitive regardless of hardware scaling. Experimental validation was performed on a Qualcomm Snapdragon 8 Gen 2 (8-core ARM) and independently reproduced on Linux x86-64 server hardware. The solver requires no cloud infrastructure and no GPU acceleration. STATEMENT OF PRIOR ART AND LICENSE TERMS (PolyForm Noncommercial Framework) 1. Statement of Prior Art This document constitutes a public disclosure of the stochastic bit-parallel Maximum Clique methodology, including its virtual register architecture, heuristic structure, and execution model.The mathematical and algorithmic concepts are released solely to establish Prior Art and prevent third-party patent claims under 35 U.S.C. § 102 and international equivalents. 2. Software License While the conceptual methods are disclosed defensively, all source code, implementations, binaries, and hardware realizations are not in the public domain and are licensed under the PolyForm Noncommercial License 1.0.0. Permitted (Non-Commercial)• Academic research and experimentation• Peer review and independent verification• Educational and non-profit use• Non-commercial open-source research implementations Condition: Publications must cite the canonical DOI or primary reference. Prohibited (Commercial)• Integration into proprietary software or hardware• Deployment in commercial systems, services, or products• Use in paid tools, platforms, or consulting workflows• Sublicensing or sale of the code or derivatives 3. Commercial Licensing Any commercial use requires explicit written authorization from the author. 4. No Code-Size Threshold (No De Minimis) The PolyForm Noncommercial License imposes no exemptions based on code length, fragment size, or proportion of reuse. Any use—partial or complete—remains fully subject to the license. 5. Anti-Snippet Laundering and Anti-Circumvention Extraction, paraphrasing, refactoring, translation, or reimplementation of any algorithmic component—including bit-parallel structures, heuristics, or execution logic—shall be considered derivative use.Attempts to evade the license through minimal reuse, language changes, functional replication, or modular embedding do not limit its applicability.This interpretation aligns with international good-faith and anti-abuse principles. 6. Presumption of Derivation Any system exhibiting substantial functional or structural similarity, developed after exposure to this work, shall be presumed derivative.The burden of proof for independent creation rests on the alleged infringing party. 7. Knowledge Contamination Exposure to the code, documentation, or technical description constitutes knowledge contamination.Subsequent implementations by exposed parties are not considered clean-room unless supported by contemporaneous evidence of prior independent development. 8. Waiver of Jury Trial To the fullest extent permitted by law, all parties waive the right to a jury trial in disputes arising from this license or related use. 9. Severability and Survival If any provision is deemed unenforceable, the remaining provisions remain in effect.The following provisions survive termination: license scope, noncommercial restrictions, anti-circumvention, presumption of derivation, knowledge contamination, intellectual property ownership, waiver of jury trial, and remedies. 10. Academic Use and Research Freedom The author expressly encourages academic and scientific use of this work. The following activities are permitted on a non-commercial basis: • Research, benchmarking, and experimental validation• Publication of scientific analyses, comparisons, or extensions• Use in university courses, laboratories, and academic projects• Inclusion in research solver portfolios• Independent theoretical or empirical study All academic use must include proper citation to the original work.
The introduction of non-fungible tokens (NFTs) has revolutionised digital ownership and asset management in the quickly changing environment of blockchain technology. NFTs are a kind of token that cannot be exchanged for another token. On the other hand, as the market for NFTs continues to grow, customers are becoming more and more interested in interoperability across various blockchain networks. Cross-chain non-fungible token markets have been developed as a result of this necessity. These marketplaces make it possible for different blockchain ecosystems to engage in transactions and interactions with one another. LayerZero and Chainlink are two technologies that are very significant in addressing the difficulty of interoperability across different chains.
A connected loopless graph is 2-edge-connected if it remains connected after the removal of at most one of its edges. Many combinatorial optimization problems seek, for a given graph with costs on its edges, a spanning subgraph satisfying certain connectivity constraints. The minimum 2-edge-connected spanning subgraph problem (2-ECSSP) is a problem of this type. It can be formulated as an integer linear program that selects edges of minimum total cost satisfying the restriction that every cut of the given graph is covered by at least two of the selected edges. This problem is known to be NP-hard. This thesis develops rounding algorithms for three variants of 2-ECSSP, focusing on rounding half-integral solutions of the corresponding linear relaxation. This family of solutions often yields the largest known integrality ratio for various subproblems of 2-ECSSP. The first problem we investigate is the half-integral 2-ECSSP with unrestricted costs. We develop a novel 5/3-rounding that, to the best of our knowledge, is the first one with a factor better than 2. Moreover, we design a reduction scheme, restricting the problem to 4-edge-connected graphs with maximum degree at most five. Then, we study the matching augmentation problem (MAP), a subproblem of 2-ECSSP in which the edge costs are either 0 or 1 and the zero cost edges define a matching. We survey a better-than-2-approximation, obtained in 2022 by Bamas, Drygala, and Svensson, presenting a comprehensive proof of their result and determining an improved factor. Additionally, we address conjectures posed in their work and present computational experiments to support our findings. Finally, we discuss the 2-edge-connected spanning multisubgraph problem (2-ECSMP), a variation of 2-ECSSP in which multiple copies of the same edge can be selected. We survey a recent work by Boyd et al. on a 4/3-rounding for the half-integral 2-ECSMP and leverage their techniques to prove novel decomposition theorems for 4-regular 4-edge-connected graphs. Finally, we pose two conjectures concerning extensions of the decomposition results, suggesting new research directions.
Existing blockchain system face scalability issues when processing massive amounts of data.These issues primarily arise due to their consensus based block generation methods.Sharding has emerged as a promising on chain solution to enhance the scalability of blockchain.This technology increases throughput by dividing the main network into several sub-networks, called shards, which can process transactions in parallel.However, implementing sharding in blockchain system presents two significant challenges: Cross shard transactions and load imbalance between different shards.Cross shard transaction refers to transactions generated between accounts belonging to different shards.Load imbalance occurs when specifical one shard processes a disproportionately higher transaction load than others.These challenges can lead to increased network delay, confirmation time, latency, and fees due to complicated inter-shard communication, thereby reducing blockchain throughput.To address these challenges, this paper proposes an innovative account relocation scheme.This scheme aims to optimize load balancing in blockchain sharding using a round robin algorithm.To validate the effectiveness of our approach, we utilized a simulator that incorporates real Ethereum data.We then compared the degree of load balancing achieved by our method against existing methods, such as schemes that use no-relocation and random relocation.Our results indicate a significant improvement in load balancing performance compared to previous approaches.