Nested Active-Time Scheduling

TL;DR

This paper introduces a 9/5-approximation algorithm for nested active-time scheduling, improving the approximation ratio for a special case where job windows are laminar, thus advancing scheduling efficiency.

Contribution

It presents the first improved approximation algorithm for laminar window scheduling, surpassing the previous 2-approximation for the general case.

Findings

Achieved a 9/5-approximation ratio for laminar window scheduling.

Demonstrated improved efficiency over previous algorithms for special cases.

Provided theoretical bounds for active-time scheduling with nested windows.

Abstract

The active-time scheduling problem considers the problem of scheduling preemptible jobs with windows (release times and deadlines) on a parallel machine that can schedule up to $g$ jobs during each timestep. The goal in the active-time problem is to minimize the number of active steps, i.e., timesteps in which at least one job is scheduled. In this way, the active time models parallel scheduling when there is a fixed cost for turning the machine on at each discrete step. This paper presents a 9/5-approximation algorithm for a special case of the active-time scheduling problem in which job windows are laminar (nested). This result improves on the previous best 2-approximation for the general case.