Error-resilient Distributed Local Verification

2026-03-21

AI Summary

This work addresses the reliability of graph property verification in distributed networks under label corruption, focusing on decision tasks such as cycle detection, acyclicity, and bipartiteness. Building upon the locally checkable labeling (LCL) model, the paper proposes a cycle-detection encoding scheme requiring only two labels and introduces ReFix, a novel general-purpose fault-tolerant framework that robustifies any local verification algorithm against localized label errors. Theoretical analysis shows that reliable verification is achievable within a (d + 2i)-hop neighborhood in the presence of i erroneous labels. Empirical evaluations demonstrate the framework’s effectiveness across multiple graph properties, while theoretical lower bounds are established relating the number of errors to the required neighborhood size for correct verification.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Graph-based Machine Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Web data provenance, reliability, and authenticity

Abstract

We study verification (decision) problems for graph properties in distributed networks under the locally checkable labeling framework, where nodes use labels (proofs) and local neighborhoods to decide acceptance or rejection. Our focus is twofold. First, we study cycle detection. While it is known that this can be verified using 3 labels with access to the 1-hop neighborhood, we introduce a novel gadget that encodes direction along a path using only 2 labels and access to a 3-hop neighborhood. This yields a cycle-detection labeling scheme with just 2 labels and may be of independent interest. Second, we consider adversarially corrupted labelings, where each node has access to a local neighborhood within which a fraction of nodes may receive erroneous labels. We introduce a general algorithmic framework, called refix, that transforms a base verification algorithm for a property P operating on labels within a d-hop neighborhood into one that tolerates up to i erroneous labels within a radius d+2i, by accessing a d+2i-hop neighborhood. We demonstrate applications to cycle detection, cycle absence, and bipartiteness, and provide lower bounds relating the number of errors to the required neighborhood size.

Problem

• distributed verification
• error resilience
• locally checkable labeling
• cycle detection
• adversarial errors

Innovation

• error-resilient verification
• locally checkable labeling
• cycle detection
• distributed graph algorithms
• refix framework