From introductory Computer Science courses you know what an algorithm is. The area algorithms (sometimes called algorithms and data structures or algorithmics) is at the core of Computer Science and deals with all aspects of the concept of algorithm design, usually with a focus on certain properties. This always includes correctness and usually performance in some form; the time complexity of an algorithm, the quality of solutions computed by an algorithm, etc. Algorithms people design concrete algorithms for specific problems, but also consider limits of computation, for instance establishing lower bound results on how efficient algorithms for particular problems can be. Algorithms people can be very mathematically oriented or can have a more applied focus. However, usually algorithms work involves both modeling of "the real world" and proofs or other formal statements concerning the algorithmic possibilities in a given setting.

If you are a Computer Science student who likes to think and to be challenged, you probably like algorithms. The central algorithms courses on the bachelor education are

• Algorithms and Data Structures,
• Algorithms and Probability
• Complexity and Computability

What all these courses and the courses at the MS level have in common is that they focus on core algorithmic problems of importance in many real-life applications. At the same time, they are based on a solid algorithmic foundation, usually with provably correct algorithms accompanied by qualitative results in the form of asymptotic time complexities or performance quarantees.

On the MS program, the following list of elective courses highlight different aspects of algorithms, listing the courses very roughly from the more theoretical (proof-oriented) to the more applied (implementation-oriented):

• Cryptology (Joan Boyar)
• Combinatorial Optimization (Jørgen Bang-Jensen)
• Online Algorithms (Lene Favrholdt)
• String Algorithms (Rolf Fagerberg)
• Advanced Data Structures (Kim S. Larsen)
• Approximation Algorithms (Lene Favrholdt) [or Heuristics and Approximation Algorithms]
• Computational Geometry (Kim S. Larsen)
• Network Programming (Jørgen Bang-Jensen)
• Algorithms in Cheminformatics (Daniel Merkle)

It is a broad field, and everyone has preferences, but if you like some of these courses, you like algorithms!

VisuAlgo visualizes many of the structures we work with in the area of algorithms.

Since you have the book anyway, you can look at some of the more advanced topics in

Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein.
Introduction to Algorithms, 4th ed.
The MIT Press, 2022.

You can of course also talk to faculty members and Ph.D. students, working on topics you are particularly interested in.

You can also attend colloquia and research seminars. It varies a lot over the year how many are scheduled, and you should be warned that most of these are talks from researcher to researchers, so they are hard to follow, but it is fine to try to show up. They usually last 45-60 minutes.

If you want to know more about algorithms at IMADA, this page gives a very brief overview. It varies, but some members of the group have more on their own home pages, and you can look at individual papers, almost all of which are listed under publications. Some of our topics are represented in the You find the subgroups in the menu.subgroups, which represent areas of algorithms where we are particularly well known in the research community.

A few surveys have been written by group members, giving overviews of a particular area. You should be warned that this is not popular science communication, but research communicated to other researchers, so it can be difficult to read.

Online Algorithms with Advice: A Survey.

Joan Boyar, Lene M. Favrholdt, Christian Kudahl, Kim S. Larsen, and Jesper W. Mikkelsen.
ACM Computing Surveys, 50(2):1-34, 2017. Article No. 19

Relative Worst-Order Analysis: A Survey.

Joan Boyar, Lene M. Favrholdt, Kim S. Larsen.
In Adventures Between Lower Bounds and Higher Altitudes - Essays Dedicated to Juraj Hromkovič on the Occasion of His 60th Birthday, volume 11011 of Lecture Notes in Computer Science, pages 216-230. Springer, 2018.

Other than guessing from courses and maybe reading a bit in addition, it is often a good idea to talk to older students, currently working on their MS thesis, and hear about their experiences.

You can also consider this list of fairly recent MS dissertation titles (and advisors), which displays quite a variety in topics, as well as in direction with regards to theory or practice.

2023

• Exact Algorithms for the Bounded Degree Vertex Cover Problem
  (Joan Boyar)
• Pathway Models in Chemical Reaction Networks
  (Jakob Lykke Andersen)
• Combinatorial Aspects of Routing Problems
  (Jørgen Bang-Jensen)
• Combinatorial Methods for Scheduling
  (Jørgen Bang-Jensen)
• Structurel and Algorithmic Aspects of Quasi-Transitive Digraphs
  (Jørgen Bang-Jensen)

2022

• Bin Covering with Limited Item Sizes
  (Lene Favrholdt, Kim Skak Larsen)
• Online Multi-Coloring of Trees and Interval Graphs
  (Lene Favrholdt, Kim Skak Larsen)
• Exact Algorithms for Maximum Independent Set in Graphs of Bounded Degree
  (Joan Boyar)
• Comparing Efficient Primality Pests
  (Joan Boyar)
• Automated Rule Inference for Systems Chemistry
  (Daniel Merkle, Jakob Lykke Andersen)
• Causality and Concurrency for Analysing Chemical and Biological Systems
  (Daniel Merkle, Jakob Lykke Andersen, Rolf Fagerberg)
• Coloring of Graphs
  (Anders Yeo)
• Domination and Total Domination in Graphs
  (Anders Yeo)
• Mathematical Programming Approaches for the Salt Spreading Problem with Side Constraints
  (Anders Yeo, Marco Chiarandini)
• Connectivity Properties of Semicomplete Digraphs
  (Jørgen Bang-Jensen, Anders Yeo)
• Minimum Spanning Tree
  (Rolf Fagerberg)

2021

• Domination and Total Domination in Graphs
  (Anders Yeo)
• Colouring in Graphs and Digraphs
  (Anders Yeo, Jørgen Bang-Jensen)
• Structural Properties of Decomposable Digraphs
  (Jørgen Bang-Jensen)
• How Feasible is a Unikernel OS for Robots?
  (Daniel Merkle, Jakob Lykke Andersen)
• Generic Implementation of Algorithms for Graph Morphism Enumeration
  (Jakob Lykke Andersen, Daniel Merkle)
• Algorithmic Cheminformatics, Quantum Chemistry, and Stochastic Simulations
  (Daniel Merkle, Jakob Lykke Andersen)
• Data Driven Game Design for VR
  (Rolf Fagerberg, Peter Schneider-Kamp)
• A Password Capability Based System with Integrated Capability based Cryptographic File System
  (Daniel Merkle, Joan Boyar)
• Algorithmic Cheminformatics and Data Science for Water Treatment
  (Daniel Merkle, Jakob Lykke Andersen)
• Choosing Intermediate Representations for a Compiler for an Operating Systems Language
  (Kim Skak Larsen)
• Aspects of Efficiency in Functional Programming Languages
  (Kim Skak Larsen)
• Oblivious Transfer in Quantum Cryptography
  (Joan Boyar)
• Linear Objective Functions for Online Problems
  (Kim Skak Larsen)

2020

• Container Orchestration Optimization Modeled by Online Bin Packing
  (Joan Boyar)
• Ferry Route Optimization
  (Marco Chiarandini, Kim Skak Larsen, Mads Bruun Larsen, Marie Lützen)
• Generation of Safe and Efficient Aircraft Departure Procedures
  (Marco Chiarandini, Kim Skak Larsen, Anders Knudsen)
• Graph Theory and FPT
  (Anders Yeo, Jørgen Bang-Jensen)
• Machine Learning for Graph Grammar Rule Prediction
  (Daniel Merkle, Arthur Zimek)
• Network Optimization with Practical Applications
  (Jørgen Bang-Jensen)
• Provably and Experimentally Efficient Multi-Way Trees with Relaxed Balance
  (Kim Skak Larsen)
• Table Reservations in Restaurants and Related Problems
  (Kim Skak Larsen, Marco Chiarandini, Arthur Zimek, Morten Frank)

2019

• Analytic Combinatorics and Boltzmann Sampling in Chemistry
  (Daniel Merkle, Markus Nebel)
• Connectivity in Graphs with Relation to the European Electrical Grid
  (Anders Yeo, Marco Chiarandini)
• Decomposition and Evaluation of Graph Transformation Rules - Exploring and Evaluating Reaction Mechanisms
  (Daniel Merkle, Jakob Lykke Andersen)
• Definition and Evaluation of Pressure in the Sport Soccer
  (Rolf Fagerberg, Mikkel Keldmann)
• Gillespie-Simulations for Graph-Grammar Models
  (Daniel Merkle, Jakob Lykke Andersen)
• Graph Canonicalization and Algorithmic Engineering
  (Daniel Merkle, Jakob Lykke Andersen)
• Optimization of the Total Fuel Price by Combinations of Flight Legs Performed by the Same Airplane
  (Jørgen Bang-Jensen)
• Theoretical and Experimental Analysis of Involved Paging Algorithms
  (Kim Skak Larsen)

2018

• Algorithmic Synthesis Planning
  (Daniel Merkle)
• Computational Synthesis Planning Using Big Data
  (Daniel Merkle)
• Generic Approaches for Group Contribution Methods
  (Daniel Merkle, Marc Hellmuth)
• Graph Transformation, Atom Tracing, and Isotope Labelling
  (Daniel Merkle)
• Online Problems with Orthogonal Resource Constraints
  (Kim Skak Larsen)

2017

• Artificial Intelligence in Action Real-Time Strategy Games
  (Rolf Fagerberg, Marco Chiarandini)
• Contributions to Flight Route Optimization
  (Marco Chiarandini, Kim Skak Larsen)
• Designing Data Structures with Relaxed Balance
  (Kim Skak Larsen)
• Dynamic Simulation on Hypergraphs
  (Daniel Merkle)
• Fixed Parameter Tractable Problems for Digraphs
  (Jørgen Bang-Jensen)
• Graph Interdiction Problems
  (Jørgen Bang-Jensen)
• Network Interdiction
  (Jørgen Bang-Jensen)
• Query Complexity for Variations of Geometric Problems
  (Kim Skak Larsen)
• Symbolic Methods for Counting Molecules
  (Daniel Merkle)
• The Entropy Compression Method
  (Jørgen Bang-Jensen)

2016

• A Permutation Group Approach to Creation of Self-Assembling Polyhedra from Single-Chain Polypeptides
  (Daniel Merkle, Wojciech Szymanski)
• Carbon Tracing in Chemical Reaction Networks
  (Daniel Merkle)
• Query Competitiveness for Problems with Uncertainty
  (Kim Skak Larsen)

2015

• Computational Complexity and Cheminformatics
  (Daniel Merkle, Rolf Fagerberg)
• DNA-Templated Computing
  (Kim Skak Larsen, Daniel Merkle)
• Lattice-Based Cryptography
  (Joan Boyar)
• Online Problems with Buffering
  (Kim Skak Larsen)
• Parallelization of Search Tree Based Algorithms
  (Daniel Merkle)
• Threshold Implementations of Small S-Boxes
  (Joan Boyar)
• Vertex Labellings with Unique Labels and Their Use in Graph Algorithms
  (Jørgen Bang-Jensen)

2014

• A Computational and Mathematical Approach to Synthesis Planning
  (Daniel Merkle)
• European Football Placement Problems - Complexities and Exact Solutions
  (Kim Skak Larsen)
• Graph Rewriting for DNA Computing
  (Daniel Merkle)
• Real-Time Fluid Simulation and Rendering in Games
  (Rolf Fagerberg)

Come talk to someone! You can drop by, and we can talk right away, if possible. Otherwise, we make an appointment. You can also send an email and make an appointment that way.