Polynomial-time scheduling on three identical machines
OpenAI research collection · 1 manuscript · Source checked 2026-10-19
OpenAI's result summary
Resolves the three-processor unit-job scheduling problem of Garey and Johnson: a deterministic polynomial-time algorithm minimizes makespan for nonpreemptive unit-length jobs with arbitrary precedence constraints on three identical parallel machines. For an explicitly given precedence graph, it decides deadline feasibility exactly and constructs a feasible schedule.
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MANUSCRIPT 01
A Polynomial-Time Algorithm for Three-Machine Unit-Job Scheduling
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…
Full source 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.
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