algorithm variant design

This work addresses the often-overlooked optimization potential in existing published algorithms, where manual refinement is typically costly and inefficient. The authors propose a two-stage AI-assisted pipeline: first, a research-capable large language model identifies recently published algorithms that meet predefined experimental criteria; second, a Claude Code agent automatically reproduces baseline implementations and iteratively optimizes the code. This study presents the first systematic application of embodied coding agents to automate performance improvements across diverse domains of published algorithms, while underscoring the indispensable human role in defining objectives, validating outcomes, and ensuring ethical transparency. Evaluated on eleven cross-domain tasks, the approach consistently achieves performance gains, with each optimization cycle completed within a single day.

Empirical studies of meta-algorithms—such as algorithm selection, configuration, and scheduling—suffer from poor reproducibility and high bias risk due to excessive degrees of freedom in experimental design and fragmented community practices. Method: This paper introduces the first systematic integration of long-standing best practices from the COSEAL community across subfields, yielding a unified, dynamically evolving methodology framework spanning the entire experimental lifecycle: problem formulation → experimental design → execution → analysis → result presentation. Grounded in empirical methodology, rigorous experimental design, statistical standards, and principles of scientific communication, it emphasizes controlled variable management, benchmark standardization, and result transparency. Contribution/Results: The framework significantly reduces experimental bias, enhances cross-study comparability, and strengthens scientific rigor. It has been adopted for onboarding new researchers and informing journal review criteria.

Algorithm engineering has long lacked a unified methodology, resulting in fragmented knowledge across subfields and poor reproducibility. To address this, this paper introduces Karl Popper’s “Three Worlds” theory—comprising ontology (clarifying problems, tasks, design, and implementation), epistemology (distinguishing descriptive from prescriptive knowledge), and methodology (systematizing knowledge evolution)—to establish the first integrated three-dimensional framework for the field. By synthesizing philosophical methodology, ontological modeling, and empirical paradigm analysis, we propose the first formal research framework for algorithm engineering, explicitly defining validity criteria for diverse scholarly contributions. This framework enhances systematicity, rigor, and cross-domain comparability in algorithm design, implementation, and evaluation. It provides foundational methodological support for disciplinary integration and advances algorithm engineering toward a mature, theory-grounded science.

Repetitive computation in change-sensitive programs—such as database queries, compilers, and real-time analytics—incurs substantial overhead and undermines complexity control. Method: We propose the “incrementalization” paradigm, formalizing incremental computation as a discrete analogue of differentiation and establishing its theoretical foundation in discrete computation. Our approach introduces an “iterate–incrementalize–implement” design framework, featuring a novel meta-level abstraction-driven model for algorithmic complexity refinement, integrating higher-order abstractions over data, control flow, and modules with formal incrementalization transformations. Contribution/Results: We deliver a reusable, formally verifiable incrementalization methodology that guarantees correctness while significantly improving computational efficiency and enhancing controllability of algorithmic complexity. The framework enables systematic, principled application of incremental computation across diverse domains, bridging theory and practice in program optimization and reactive systems.

This work systematically evaluates the capability boundaries of Llama 3.1 405B on natural language-to-multilingual executable code generation, focusing on algorithmic problem solving and fundamental data structure tasks. To address limitations in cross-lingual code synthesis and robustness, we propose a synergistic approach integrating context-aware prompt engineering, multilingual code fine-tuning, and dynamic test-time validation. On standard benchmarks—including HumanEval and MBPP—our method achieves state-of-the-art performance, attaining >82% pass@1 accuracy on medium-difficulty algorithmic problems. We further provide the first empirical evidence that Llama 3.1 405B exhibits strong generalization on classical computer science problems (e.g., sorting, graph traversal), yet its accuracy drops substantially in frontier domains such as quantum computing and bioinformatics. These findings offer rigorous empirical support and a concrete technical pathway for large language model–driven programming assistance and computational education.

Existing AI approaches to problem solving either rely on costly model-centric strategies or employ fragmented prompting techniques, lacking a unified, interpretable, and efficient algorithmic reasoning framework. This work proposes MAS-Algorithm, the first systematic application of multi-agent systems to algorithmic programming problem solving. Inspired by competitive programming, it constructs a modular and collaborative workflow that enables structured reasoning and seamless integration with external tools. The method demonstrates strong scalability and generality, achieving average pass rate improvements of 6.48% on a newly curated benchmark and 4.72% on LiveCodeBench-Pro. Notably, individual agents contribute performance gains as high as 27.7%, significantly outperforming baseline approaches such as parameter-efficient fine-tuning.

This work addresses the challenge in scientific computing where models struggle to transfer knowledge from individual tasks to broader, reusable capabilities. The authors propose SciConsolidate, a novel framework that, for the first time, extracts procedural knowledge from runtime success and failure trajectories and employs a development-validation gating mechanism to filter effective knowledge. To bridge the gap between abstract knowledge and executable code, the approach integrates failure-driven synthesis of unanswerable queries with strong-model-guided concretization supervision. Additionally, a matched teacher-branch architecture is introduced to significantly enhance the performance of smaller models. Experimental results demonstrate that Qwen3.5-9B achieves gains of 6.25 and 3.89 points over program-free supervised fine-tuning—and improvements of 11.25 and 5.62 points over the base model—on main tasks and sub-steps, respectively, validating the efficacy of the proposed methodology.

This work proposes a formalization of algorithms within an intensional computability framework and clarifies their relationship to implementations in computational models. Treating computational models as monoid actions on configuration spaces, programs are modeled as dynamical systems constrained by such actions. Algorithms are defined as finite directed graphs of partial maps over edge-labeled abstract data structures, explicitly separating control flow from data operations. By leveraging tools from category theory, dynamical systems theory, and graph theory, the approach constructs a rigorous semantic framework that, for the first time, treats algorithms as abstract specifications of computational behavior and precisely characterizes the structure-preserving implementation relation between programs and algorithms, thereby deepening our understanding of the nature of computation.

This work addresses the challenge that small language models often fail to reliably execute multi-step, dependency-rich structured graph algorithms due to error accumulation. The authors frame algorithm execution as a closed-loop prediction task, wherein the model iteratively selects operations based on the current graph state and evaluates its overall behavior through full rollbacks. Departing from conventional step-isolated evaluation, this closed-loop rollback paradigm reveals that strong single-step prediction accuracy does not necessarily ensure stable global execution. Experimental results demonstrate that suitably adapted small models can reliably perform algorithms such as traversal and coloring, yet remain vulnerable to cumulative errors in weighted graph algorithms. These findings underscore the necessity and efficacy of the proposed closed-loop evaluation framework for assessing and improving algorithmic reasoning in language models.

Traditional AI systems rely on fixed monolithic models, which struggle to dynamically allocate resources, decompose tasks, or update knowledge in response to varying inputs, leading to degraded performance and increased costs. This work proposes the first system-level design methodology for distributed composite AI systems, formulating a design space through workflow topologies and configuration choices and identifying eight core design patterns. The framework jointly optimizes model selection and runtime parameters, enabling task decomposition, multi-model orchestration, and explicit control logic, thereby facilitating a shift from static monolithic architectures toward dynamic, composable, and adaptive ones. Evaluated across three case studies, the approach reduces latency by up to 60% and cost by up to 71%, with only a 2.5–4 percentage point drop in accuracy.