Combinatorial optimisation problems arise in many fields, from logistics and network design to machine learning and bioinformatics. Most classical formulations are NP-hard, rendering exact ...

Abstract: Noncommutative constraint satisfaction problems (CSPs) are higher-dimensional operator extensions of classical CSPs. Their approximability remains largely unexplored. A notable example of a ...

This course studies approximation algorithms – algorithms that are used for solving hard optimization problems. Such algorithms find approximate (slightly suboptimal) solutions to optimization ...

Abstract: We address the problem on uniform parallel batch machines to minimize makespan where each job is restricted to a specific subset of machines, known as its processing set. Batch machines have ...

This project explores the NP-hard problem of scheduling unrelated parallel machines, a significant challenge in optimizing resource utilization. Specifically, it focuses on efficiently assigning ...

This paper studies the fair range clustering problem in which the data points are from different demographic groups and the goal is to pick \(k\) centers with the minimum clustering cost such that ...