# Some complexity and approximation results for coupled-tasks scheduling problem according to topology

## TL;DR

This paper investigates the complexity and approximation algorithms for scheduling coupled-tasks with compatibility constraints defined by specific topologies, focusing on bipartite graphs and stretched tasks to develop efficient solutions.

## Contribution

It introduces new polynomial-time approximation algorithms for intractable coupled-tasks scheduling problems under certain compatibility graph topologies.

## Key findings

- Polynomial-time approximation algorithms for bipartite compatibility graphs.
- Complexity results for coupled-tasks scheduling with specific topologies.
- Analysis of stretched coupled-tasks with equal sub-task and idle times.

## Abstract

We consider the makespan minimization coupled-tasks problem in presence of compatibility constraints with a specified topology. In particular, we focus on stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution time and idle time duration. We study several problems in framework of classic complexity and approximation for which the compatibility graph is bipartite (star, chain,. . .). In such a context, we design some efficient polynomial-time approximation algorithms for an intractable scheduling problem according to some parameters.