# A Comparison of Random Task Graph Generation Methods for Scheduling Problems

## TL;DR

This paper compares different random task graph generation methods for scheduling problems, analyzing their properties and impact on heuristic performance to ensure fair and relevant instance creation.

## Contribution

It provides an in-depth analysis of existing generation methods and introduces property-based criteria to generate challenging instances without bias.

## Key findings

- Mass measure quantifies graph decomposability.
- Sub-exponential time complexity for generating difficult instances.
- Generation method impacts heuristic effectiveness.

## Abstract

How to generate instances with relevant properties and without bias remains an open problem of critical importance for a fair comparison of heuristics. In the context of scheduling with precedence constraints, the instance consists of a task graph that determines a partial order on task executions. To avoid selecting instances among a set populated mainly with trivial ones, we rely on properties that quantify the characteristics specific to difficult instances. Among numerous identified such properties, the mass measures how much a task graph can be decomposed into smaller ones. This property, together with an in-depth analysis of existing random task graph generation methods, establishes the sub-exponential generic time complexity of the studied problem. Empirical observations on the impact of existing generation methods on scheduling heuristics concludes our study.