A Parameterized-Complexity Framework for Finding Local Optima

Thu, 01 Jan 2026 00:00:00 +0000

Fine-Grained Complexity of Computing Degree-Constrained Spanning Trees

Thu, 01 Jan 2026 00:00:00 +0000

Matrix Editing Meets Fair Clustering: Parameterized Algorithms and Complexity

Thu, 01 Jan 2026 00:00:00 +0000

Not All Degree Constraints Are Created Equal when Computing Spanning Trees

Thu, 01 Jan 2026 00:00:00 +0000

Parameterized Complexity of Efficient Sortation

Thu, 01 Jan 2026 00:00:00 +0000

Conflict-Free Coloring: Graphs of Bounded Clique-Width and Intersection Graphs

Mon, 01 Jan 2024 00:00:00 +0000

Generating All Invertible Matrices by Row Operations

Mon, 01 Jan 2024 00:00:00 +0000

Parameterized Analysis in Artificial Intelligence

Mon, 01 Jan 2024 00:00:00 +0000

Funding organization: The Austrian Science Funds, FWF
Project number: Y 1329 START-Programm (ParAI)
Grant DOI: 10.55776/Y1329

Project Team

Picture credits: Soeren Nickel, 2020

Research Statement

Parameterized complexity theory is a well-established paradigm used for the fine-grained analysis of computational problems. Such analysis can provide efficient algorithms for these problems by exploiting subtle structural properties of relevant inputs, as well as powerful lower bounds that rule out efficient algorithms even for severely restricted instances. Parameterized complexity analysis has found great success across numerous fields of computer science, with notable examples including graph algorithms, computational geometry, database theory, computational logic and constraint satisfaction. In the highly prominent fields of artificial intelligence (AI) and machine learning (ML) – areas which have become an ubiquitous part of today’s society – we see a distinct lack of foundational research targeting the fine-grained, parameterized complexity of fundamental problems. The goal of this six-year project is to change this.

A Parameterized Toolbox for Problems in AI and ML

One main objective of this project is the development of new innovative tools and machinery that allows us to apply the parameterized complexity framework in this setting. Indeed, most of the existing tools developed in parameterized complexity theory are designed to work in the setting of discrete problems on graphs. On the other hand, many problems of interest in AI and ML do not admit straightforward graph representations and/or contain non-discrete components. The development of the required tools will then go hand in hand with obtaining new algorithms and matching lower bounds for the studied problems.

The k-Opt Algorithm for the Traveling Salesman Problem Has Exponential Running Time for k \(\geq\) 5

Mon, 01 Jan 2024 00:00:00 +0000

Phuc Hung Hoang | AC Group | TU Wien

A Parameterized-Complexity Framework for Finding Local Optima

Fine-Grained Complexity of Computing Degree-Constrained Spanning Trees

Matrix Editing Meets Fair Clustering: Parameterized Algorithms and Complexity

Not All Degree Constraints Are Created Equal when Computing Spanning Trees

Parameterized Complexity of Efficient Sortation

Conflict-Free Coloring: Graphs of Bounded Clique-Width and Intersection Graphs

Generating All Invertible Matrices by Row Operations

Parameterized Analysis in Artificial Intelligence

Project Team

Research Statement

A Parameterized Toolbox for Problems in AI and ML

The k-Opt Algorithm for the Traveling Salesman Problem Has Exponential Running Time for k \(\geq\) 5