Pathological Cases for a Class of Reachability-Based Garbage Collectors

Although existing garbage collectors (GCs) perform extremely well on typical programs, there still exist pathological programs for which modern GCs significantly degrade performance. This observation begs the question: might there exist a 'holy grail' GC algorithm, as yet undiscovered, guaranteeing both constant-length pause times and that memory is collected promptly upon becoming unreachable? For decades, researchers have understood that such a GC is not always possible, i.e., some pathological behavior is unavoidable when the program can make heap cycles and operates near the memory limit, regardless of the GC algorithm used. However, this understanding has until now been only informal, lacking a rigorous formal proof. This paper complements that informal understanding with a rigorous proof, showing with mathematical certainty that every GC that can implement a realistic mutator-observer interface has some pathological program that forces it to either introduce a long GC pause into program execution or reject an allocation even though there is available space. Hence, language designers must either accept these pathological scenarios and design heuristic approaches that minimize their impact (e.g., generational collection), or restrict programs and environments to a strict subset of the behaviors allowed by our mutator-observer-style interface (e.g., by enforcing a type system that disallows cycles or overprovisioning memory).