Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 124-01. A Polynomial-Time Algorithm for Three-Machine Unit-Job Scheduling
Manuscript map · lines 4845–4854
OpenAI@2026-10-07#rem:oai-p-124-01
Authors: OpenAI. Family 124.
Title: A Polynomial-Time Algorithm for Three-Machine Unit-Job Scheduling.
Abstract: We give a uniform deterministic polynomial-time algorithm for scheduling unit-length jobs with arbitrary precedence constraints on three identical parallel machines. The algorithm constructs a schedule of minimum makespan and decides exactly whether all jobs can finish by a specified deadline. The proof reorganizes feasible schedules into intervals whose job sets have descriptions of bounded size. A dynamic program searches a family containing polynomially many such descriptions. Global boundary conditions and simplification of inherited information keep the descriptions bounded throughout the decomposition.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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