Extension of the classical work-stealing bound to paulikit

Determine whether the classical work-stealing time bound, expressed as T_1/P + O(T_\infty), extends to paulikit’s flat thread-pool scheduler, which uses statically sliced workers that steal directly from one another’s queues without recursively spawning threads.

Background

The paper analyzes paulikit’s parallel decomposition using Work–Span and Brent-style bounds, but distinguishes these general scheduling bounds from the stronger classical work-stealing guarantee of T_1/P + O(T_\infty). That guarantee is established for fully strict computations, where recursive spawn trees return through their corresponding parent joins.

paulikit instead employs a flat pool of statically sliced workers that can steal work directly from one another’s queues and does not spawn new threads recursively. Because this scheduler does not match the model covered by the classical theorem, the paper leaves unresolved whether the theorem’s guarantee applies to paulikit’s implementation.

References

This avoids work-stealing's degenerate failure mode (stealing accomplishing nothing when all work originates from one shared queue, rather than from each worker's own), but it is not the model the theorem was proven for, so whether the classical bound's guarantee extends to paulikit's own scheduler is left open here, not asserted either way.

— Pauli Decomposition by Character Theory: A Memory-Bounded Algorithm for Qubits and Qudits  (2610.08299 - Khellat et al., 6 Oct 2026) in Section 5, Section 5.1.1 “Parallelism ceiling and its limits” (label sec:scope-and-limits)