Problem
Research questions and friction points this paper is trying to address.
open-shop scheduling
unavailability interval
makespan
FPTAS
An FPTAS for Two-Machine Open-Shop Scheduling with a Single Unavailability Interval
🤖 AI Summary
研究了两台机器开放车间调度问题，其中一台机器在固定时间段内不可用。通过设计首个完全多项式时间近似方案（FPTAS）来最小化总完工时间。
📝 Abstract
We consider the two-machine open-shop scheduling problem in which one machine is unavailable during a fixed interval. We study the resumable setting: an operation interrupted by the unavailability interval may resume, without penalty, when the machine becomes available. The objective is to minimize the makespan. Although the problem is NP-hard and several approximation algorithms are known, whether it admits a fully polynomial-time approximation scheme (FPTAS) has remained open for two decades. We resolve this question affirmatively by giving the first FPTAS, thereby strengthening the previously known polynomial-time approximation scheme (PTAS). As an intermediate result, we develop a new pseudo-polynomial dynamic program with seven state dimensions, improving on the ten-dimensional formulation in the literature.
Innovation
Methods, ideas, or system contributions that make the work stand out.
FPTAS
open-shop scheduling
unavailability interval
dynamic program
state dimensions
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