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A Polynomial-Time Algorithm for Three-Machine Unit-Job Scheduling

OpenAI

OpenAI Mathopenai-math/A-polynomial-time-algorithm-for-three-machine-unit-job-schedulingSep 24, 2026cs.CCAI-generatedscore 0

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…

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