distributed algorithm design

This work addresses foundational challenges in distributed systems—namely, formal modeling, algorithm design, correctness verification, and characterization of inherent limitations. It introduces a unified mathematical framework grounded in concurrent models such as I/O automata; establishes seminal impossibility results, including the FLP theorem; and develops systematic methodologies for proving inductive invariants of distributed algorithms and analyzing their complexity and lower bounds. The work identifies and corrects logical flaws in several classical algorithms, clarifying their fundamental constraints under asynchrony and failures. These contributions have been applied to rigorous modeling and reliability verification of distributed databases, wireless communication protocols, and biological distributed systems. By bridging theory and practice, the research provides a general methodological foundation that advances both theoretical understanding and industrial deployment of distributed systems. (149 words)

This work addresses deterministic graph algorithms in the synchronous message-passing model, focusing on leveraging potentially erroneous predictions to accelerate computation while ensuring robustness when predictions fail. We introduce the first prediction-augmented paradigm tailored to distributed graph algorithms, featuring a graph-structure-aware error metric and a generic construction template that achieves provably optimal trade-offs between speedup and robustness. Our method integrates prediction error modeling, hierarchical activation, and local adaptive decision-making, and applies to fundamental problems including maximal independent set (MIS), maximum matching (MM), (Δ+1)-vertex coloring, and (2Δ−1)-edge coloring. Notably, we provide theoretically optimal prediction-augmented algorithms for MIS on general graphs and rooted trees. The framework establishes a new theoretical foundation for distributed graph learning and prediction-driven systems, delivering both rigorous guarantees and practical algorithmic tools.

Distributed systems education faces challenges of high conceptual barriers and fragmented practical resources. To address these, this paper proposes a dual-track pedagogical paradigm—“principle-driven + full-stack implementation”—to systematically construct a comprehensible, verifiable, and extensible teaching framework. We implement 12 canonical distributed algorithms—including Paxos, Raft, and Gossip—in Python and Rust, augmented by formal modeling, interactive simulation, and a lightweight message-passing framework. The approach yields over 30 executable examples and visualization-enabled debugging tools. Crucially, we pioneer a modular, step-by-step verifiable code representation of distributed protocols, substantially reducing cognitive load for learners and instructors alike. Evaluated in graduate-level practice courses across multiple universities, the materials serve as an adopted textbook and provide a unified, theory-to-engineering learning pathway for learners with diverse technical backgrounds.

This work addresses the longstanding challenge of reconciling theoretical correctness with practical efficiency by introducing Algorithmist, a multi-agent autonomous research system built upon GitHub Copilot. Through an iterative research-review cycle, Algorithmist collaboratively performs algorithm design, formal verification, proof-guided code generation, and consistency validation. The system establishes a scalable paradigm for provably correct algorithm synthesis by integrating large language models, structured natural-language proof representations, and formal verification techniques to generate algorithms tailored to specific datasets and deployment scenarios. In applications to privacy-preserving data analysis and clustering tasks, Algorithmist automatically produces novel algorithms that simultaneously offer rigorous theoretical guarantees and strong empirical performance, uncovers previously overlooked proof flaws in existing work, and achieves state-of-the-art results in several settings.

To address the insufficient co-optimization of scalability and system stability in large-scale matrix computations on distributed-memory supercomputing platforms, this paper proposes the Block-Recursive Matrix Algorithm (BRMA) framework. BRMA uniquely integrates recursive block decomposition with distributed dynamic runtime control, incorporating task-graph–driven scheduling, a decentralized consensus protocol, and dynamic load rebalancing. Evaluated on a thousand-node cluster, BRMA achieves near-linear strong scaling, reduces communication overhead by 40%, and enables millisecond-scale fault recovery—significantly enhancing both scalability and fault tolerance. Its core contribution lies in unifying algorithmic scalability with system-level robustness, establishing a high-reliability, self-adaptive computational paradigm for exascale scientific computing.

This work addresses the challenge of simultaneously minimizing worst-case communication overhead and computational load for general functions admitting d-ary decompositions in distributed computing. The authors propose a deterministic Interweaved Clique (IC) assignment framework grounded in combinatorial design theory. This approach circumvents the restrictive existence conditions of Steiner systems, thereby revealing for the first time the fundamental scaling laws of the problem over a significantly broader range of parameters, while permitting modest heterogeneity in workers’ storage loads. The constructed IC scheme achieves communication cost within a constant factor of 4e from the information-theoretic lower bound and maintains order-wise optimal computation load.

This work addresses the disconnect between modular application design and execution in edge and cloud computing, particularly the challenges of uniformly modeling computational units, data sharing, and event dependencies. To bridge this gap, the paper proposes a domain-specific visual graph editor that enables users to define data and control flows through three core abstractions: kernel functions, shared memory nodes, and event triggers. The tool automatically generates deployable, machine-readable representations from these visual models. By integrating explicit execution semantics, modular design, and one-click deployment within a unified interface—combining visual modeling, domain-specific language (DSL) abstractions, event-driven architecture, and distributed shared memory—it significantly enhances the comprehensibility of execution order and dependencies. Evaluations in scenarios such as federated learning demonstrate its superior semantic expressiveness and direct deployability compared to general-purpose diagramming tools and conventional workflow editors.

This work addresses the challenge of parameterized verification for asynchronous round-based distributed algorithms, which is complicated by the infinite-state nature of individual processes. While the problem is shown to be undecidable, this paper presents the first reduction to LTL model checking over finite counter systems, enabling complete verification of safety and liveness properties for arbitrarily many processes. By integrating this reduction with LTL model checking and the symbolic model checker nuXmv, the approach successfully verifies several asynchronous round-based consensus and leader election algorithms, demonstrating both feasibility and effectiveness.

This work addresses the challenge of achieving both correctness and efficiency in distributed computing under extreme adversarial conditions where the fraction of malicious workers can approach one (i.e., any constant β < 1). To this end, the authors propose a supervised distributed computing paradigm in which a trusted supervisor orchestrates task assignment and delegates verification to honest nodes. By integrating directed acyclic graph–based task scheduling, a lightweight output verification protocol, and a probabilistic task allocation strategy, the system guarantees overall computational correctness while ensuring that the expected computational overhead incurred by honest nodes approaches the cost of executing a task once. This approach substantially outperforms conventional master-worker or peer-to-peer architectures in terms of efficiency under high adversarial presence.

This work addresses the limitations of traditional numerical array programs, which rely on manual parallelization constrained by static optimizations or explicit annotations, resulting in coarse-grained parallelism and poor adaptability to heterogeneous hardware. The paper proposes a self-optimizing Virtual Processor (VP) that automatically and dynamically parallelizes entire program regions at runtime through a decentralized network of collaborating execution segments, without developer intervention. Its key innovation lies in parallelizing and distributing the scheduling process itself, integrating dependency-driven local decisions, heterogeneity-aware task placement and data movement, and support from the ILNumerics.ONAL instruction set. This approach preserves sequential semantics while enabling automatic parallelism extraction across large-scale program regions, achieving low-latency strong scaling on local heterogeneous systems for a broad range of workloads—from latency-sensitive small operations to large data-parallel tasks—without requiring explicit parallel programming.