Bag-of-Tasks Scheduling on Related Machines

TL;DR

This paper presents an online scheduling algorithm for related machines that minimizes weighted completion time, achieving a competitive ratio of O(K^3 log^2 K) without prior knowledge of job sizes.

Contribution

It introduces a novel non-clairvoyant scheduling algorithm with a proven competitive ratio for complex machine-job configurations.

Findings

Achieves an O(K^3 log^2 K)-competitive ratio in non-clairvoyant setting.

Uses dual-fitting analysis on a precedence-constrained LP relaxation.

Addresses scheduling with concurrent tasks on related machines.

Abstract

We consider online scheduling to minimize weighted completion time on related machines, where each job consists of several tasks that can be concurrently executed. A job gets completed when all its component tasks finish. We obtain an $O(K^3 \log^2 K)$-competitive algorithm in the non-clairvoyant setting, where $K$ denotes the number of distinct machine speeds. The analysis is based on dual-fitting on a precedence-constrained LP relaxation that may be of independent interest.