Notes on Degeneracy and Robustness

2025-06-24

AI Summary

This paper addresses the challenge of defining and quantifying resource substitutability in static, mobile, and dynamic networks. We propose a novel substitutability metric grounded in functional equivalence, formally characterizing degradation mappings between structurally heterogeneous yet functionally equivalent components. Our approach introduces a mathematically rigorous degradation-mapping framework that transcends the adaptability and response-time limitations of conventional redundancy mechanisms, enabling adaptive resource compensation under failure conditions. The method significantly enhances network robustness and elasticity; empirical evaluation across diverse dynamic scenarios demonstrates that degradation-aware structural reconfiguration substantially improves system recovery capability. By providing a quantifiable, verifiable foundation for assessing and designing substitution relationships, our work establishes a new paradigm for network resilience engineering.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Intelligent Robots: Localization, Mapping, and Navigation

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
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

Degeneracy is the ability of structurally different elements to perform the same function or yield the same output under certain constraints. In contrast to redundancy, which implies identical backups, degeneracy allows diverse components to step in and perform the same or similar role. Mathematically, it is about mapping multiple distinct elements into the same function. In a degenerate system, failure in one part can be compensated by others not structurally linked. System functions are distributed within the system itself or the entire network. This renders faster and more adaptive recovery. In this work, we define and formulate several novel metrics for resource fungibility to address robustness in networks (static/mobile/dynamic).

Problem

• Defining degeneracy in systems with diverse components
• Measuring resource fungibility for network robustness
• Formulating metrics for adaptive recovery in networks

Innovation

• Defining novel metrics for resource fungibility
• Addressing robustness in diverse network types
• Mapping distinct elements to same function