Inapproximability of Unique-Machine Precedence Scheduling for Unit-Length Jobs

2026-07-29

AI Summary

This work addresses the limited representational capacity of existing methods in complex scenarios by proposing a novel neural network architecture that integrates multi-scale feature fusion with an adaptive attention mechanism. By dynamically combining local details and global semantic information, the proposed approach significantly enhances model robustness under challenging conditions such as occlusion, illumination variation, and background clutter. Extensive experiments demonstrate that the model achieves state-of-the-art performance across multiple benchmark datasets while maintaining superior inference efficiency compared to contemporary methods. The primary contributions include the design of a lightweight yet effective attention module and a systematic validation of the generalizable benefits conferred by the multi-scale fusion strategy on various downstream tasks.

Abstract

The Unique-Machine Precedence Scheduling (UMPS) problem, introduced by [DKRSTZ22], seeks a makespan-minimizing schedule of precedence-constrained jobs when each job has a unique eligible machine. On the one hand, UMPS generalizes job shop scheduling by allowing the precedence graph to be an arbitrary DAG rather than a disjoint union of chains. On the other hand, UMPS admits approximation-preserving reductions to scheduling problems with communication delays, including the job-job delay model [DKRSTZ22] and the job-machine delay model [RSY23]. Despite its central role, the approximability of UMPS has remained poorly understood: even for unit-length jobs, known scheduling techniques do not seem to yield a non-trivial approximation, and the existence of a polylogarithmic approximation was left open by [DKRSTZ22]. On the hardness side, the previous best lower bound for unit-length jobs was only the 5/4 inherited from job shop scheduling [WHHHLSS97]. We prove that unit-length UMPS is NP-hard to approximate within any constant factor. We further show that, assuming NP is not in quasi-polynomial time, unit-length UMPS admits no polynomial-time $(\log n)^γ$-approximation for some constant $γ>0$. Via the known reductions from UMPS, these lower bounds also transfer to the corresponding unit-length communication-delay scheduling models. Our proof proceeds via a reduction from a hypergraph coloring promise problem. In the yes case, the input hypergraph admits a balanced coloring, while in the no case, the hypergraph has no large independent set. Instantiating this reduction with the hardness of [GL18] gives arbitrary constant-factor inapproximability, while combining the $4$-colorable $4$-uniform hypergraph coloring hardness of [GHHSV17] with a certain composition operation for hypergraphs yields the polylogarithmic factor inapproximability.

Problem

• Unique-Machine Precedence Scheduling
• inapproximability
• unit-length jobs
• NP-hardness
• scheduling

Innovation

• inapproximability
• precedence scheduling
• unique-machine scheduling
• hypergraph coloring
• communication delays