# Greed Works -- Online Algorithms For Unrelated Machine Stochastic Scheduling

## TL;DR

This paper presents new combinatorial online algorithms for stochastic unrelated machine scheduling that achieve competitive ratios comparable to previous methods, with performance bounds depending on job variability.

## Contribution

It introduces purely combinatorial online algorithms for stochastic unrelated machine scheduling, extending dual fitting techniques to this stochastic, nonpreemptive setting.

## Key findings

- Competitive ratio of 4 for deterministic processing times without release times.
- Competitive ratio of 7.216 for deterministic processing times with release times.
- Performance bounds depend linearly on the squared coefficient of variation.

## Abstract

This paper establishes performance guarantees for online algorithms that schedule stochastic, nonpreemptive jobs on unrelated machines to minimize the expected total weighted completion time. Prior work on unrelated machine scheduling with stochastic jobs was restricted to the offline case, and required linear or convex programming relaxations for the assignment of jobs to machines. The algorithms introduced in this paper are purely combinatorial. The performance bounds are of the same order of magnitude as those of earlier work, and depend linearly on an upper bound on the squared coefficient of variation of the jobs' processing times. Specifically for deterministic processing times, without and with release times, the competitive ratios are 4 and 7.216, respectively. As to the technical contribution, the paper shows how dual fitting techniques can be used for stochastic and nonpreemptive scheduling problems.