Minimizing the Weighted Makespan with Restarts on a Single Machine

2025-10-10

AI Summary

This paper studies the single-machine scheduling problem with restarts—where interrupted jobs must be restarted from scratch—to minimize the maximum weighted completion time. Methodologically, it integrates online scheduling design, modeling of restart constraints, and competitive analysis techniques, employing constructive adversarial strategies and rigorous performance proofs. The contributions are threefold: (i) it establishes the first lower bound of 1.4656 on the competitive ratio for deterministic online algorithms for the general problem; (ii) for the special case of equal-length jobs, it proposes a novel online algorithm achieving a competitive ratio strictly better than 1.3098; and (iii) it derives an improved lower bound of 1.2344 for this equal-length setting. Collectively, these results significantly advance the theoretical understanding of this classical scheduling problem under restart constraints.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Machine Learning: Online Learning & Bandits
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Research challenges in human and human-AI computation
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

We consider the problem of minimizing the weighted makespan on a single machine with restarts. Restarts are similar to preemptions but weaker: a job can be interrupted, but then it has to be run again from the start instead of resuming at the point of interruption later. The objective is to minimize the weighted makespan, defined as the maximum weighted completion time of jobs. We establish a lower bound of 1.4656 on the competitive ratio achievable by deterministic online algorithms. For the case where all jobs have identical processing times, we design and analyze a deterministic online algorithm that improves the competitive ratio to better than 1.3098. Finally, we prove a lower bound of 1.2344 for this case.

Problem

• Minimizing weighted makespan on single machine with restart constraints
• Establishing competitive ratio bounds for deterministic online algorithms
• Improving algorithm performance for jobs with identical processing times

Innovation

• Single machine scheduling with restart capability
• Deterministic online algorithm for weighted makespan
• Lower bound analysis for competitive ratio limits