# Bounds and approximation results for scheduling coupled-tasks with compatibility constraints

## TL;DR

This paper establishes bounds and develops an approximation algorithm for scheduling coupled-tasks with compatibility constraints, focusing on cases where the constraints form a quasi split-graph topology, under classical complexity assumptions.

## Contribution

It provides new bounds and a polynomial-time approximation algorithm for a specific compatibility graph topology in coupled-tasks scheduling.

## Key findings

- Established lower and upper bounds under complexity hypotheses
- Developed an efficient approximation algorithm for quasi split-graph compatibility
- Analyzed the problem's complexity in different graph topologies

## Abstract

This article is devoted to propose some lower and upper bounds for the coupled-tasks scheduling problem in presence of compatibility constraints according to classical complexity hypothesis ($\mathcal{P} \neq \mathcal{NP}$, $\mathcal{ETH}$). Moreover, we develop an efficient polynomial-time approximation algorithm for the specific case for which the topology describing the compatibility constraints is a quasi split-graph.