Algorithmic self-repair: frontiers in fault-tolerant computation

How can algorithms continue to function when confronted with faults, noise, and malicious behavior? This question lies at the heart of resilient computation, a challenge addressed by multiple traditions but rarely examined through a unified lens. In this article, we introduce the concept of algorithmic self-repair as a framework for understanding how algorithms detect, mitigate, and recover from failures. We compare five major classes of algorithmic self-repair: (1) self-stabilizing algorithms that guarantee convergence from arbitrary states; (2) self-healing graph algorithms that preserve connectivity under dynamic failures; (3) error-resilient online algorithms that sustain competitiveness despite uncertain or corrupted inputs; (4) redundancy-based and probabilistic repair techniques that achieve robustness through replication or stochastic correction; and (5) Byzantine fault-tolerant algorithms that maintain correctness even in the presence of adversarial participants. By consolidating these approaches into a shared taxonomy, we highlight their guiding principles, strengths, and trade-offs. The result is not merely a survey but a structured foundation and roadmap for advancing resilient computation, positioning algorithmic self-repair as a frontier where fault tolerance becomes a defining design principle of algorithms.