Duncan Adamson

Postdoctoral researcher at the University of Göttingen studying Theoretical Computer Science

Contact Information

Address:   Institute for Computer Science, Goldschmidtstraße 7, 37077 Göttingen
E-mail:   duncan.adamson@cs.uni-goettingen.de
Photo

About

I am currently a postdoctoral researcher working on problems in Combinatorics on words, in the Theoretische Informatik group, at the University of Göttingen. Previously I was a postdoctoral researcher at the Icelandic Centre of Excellence in Theoretical Computer Science at Reykjavik University studying distributed colouring problems. Prior to coming to Iceland, I was a postgraduate researcher at the Department of Computer Science, in the algorithms and complexity research group. My PhD thesis is titled Algorithmic and Combinatorial Problems in Crystal Structure Prediction, supervised by Prof. Igor Potapov, with secondary supervisors Matthew Dyer and Vladimir Gusev. I was funded by the Leverhulme Research Centre for Functional Materials Design. Previously, I completed my undergraduate studies at the University of Glasgow, with my masters project supervised by David Manlove. My full CV is available here. A graph of my Mathematical Genealogy can be found here.

Research Interests

Combinatorics on words: My interest on combinatorics on words has been primarily motivated on representing real world objects within a discrete space. In particular, I am been interested in capturing symmetry on words, such as reflective and, in the multidimensional setting, translational symmetries. Going forward I would like to extend more results from one dimension into the multidimensional setting.

k-centre problem for implicitly defined objects (such as graphs and words): Many classes of combinatorial objects can be represented as a weighted graph using some similarity measure to assign weights to the edges. For large graphs, for instance the set of all words of length n, generating the whole graph is impractical. To this end, we seek to take a set of representative samples from the graph. The idea behind the k-centre problem for implicitly defined graphs is to take k samples from some graph that allow the local properties to be determined. At present I have worked this problem for (multidimensional) words, using the overlap distance between subwords as the distance. Going forward I would like to study more complex objects.

Crystal Structure Prediction: During my PhD I have focused on the problem of predicting the structures of Crystals from first principles. My main results has been on the hardness of this problem, and more recently on approaches to solving similarly motivated problems. Move forward I would like to show undecidability for the general version of this problem

Temporal Graphs: I have recently began working on the problem of harmonious colourings in the setting of temporal graphs. The initial results have shown that this is a highly challenging problem even when the underlying graph is a path. The next steps in the project would be to look at solutions to this problem when each time step has been solved.

Stable Matchings: During my Masters (dissertation is available here), I worked on the stable matching problem for incomplete lists with ties. My main result was providing new bounds on the number of blocking pairs for maximum matchings in this setting. Moving forward I would be interested in obtaining similar results for more complex settings such as the kidney exchange problem.

Publications

A full bib file for all published work can be found here and my dblp profile found here.
  1. The k-center Problem for Classes of Cyclic Words
    Duncan Adamson, Argyrios Deligkas, Vladimir V. Gusev, Igor Potapov
    To appear at SOFSEM 2023.
  2. The Complexity of Periodic Energy Minimisation
    Duncan Adamson, Argyrios Deligkas, Vladimir V. Gusev, Igor Potapov
    Presented at MFCS 2022.
  3. Ranking Binary Unlabelled Necklaces in Polynomial Time.
    Duncan Adamson
    Presented at DCFS 2022. Full version available on arXiv.
  4. Faster exploration of some temporal graphs.
    Duncan Adamson, Vladimir V. Gusev, Dmitriy Malyshev, Viktor Zamaraev
    Presented at SAND 2022.
  5. Ranking Bracelets in Polynomial Time.
    Duncan Adamson, Argyrios Deligkas, Vladimir V. Gusev, Igor Potapov
    Presented at CPM 2021. Full version available on arXiv.
  6. On the Hardness of Energy Minimisation for Crystal Structure Prediction.
    Duncan Adamson, Argyrios Deligkas, Vladimir V. Gusev, Igor Potapov
    Presented at SOFSEM 2020, Journal version published in Fundamenta Informaticae. Full version also available on arXiv.

Talks

SOFSEM 2023   The k-Centre problem for necklaces
ACTO Group Seminar 2022   The k-centre problem for classes of necklaces
DCFS 2022   Ranking Binary Unlabelled Necklaces
SAND 2022   Faster Exploration Of Some Temporal Graphs
HI Mathematics Seminar Series 2022   Combinatorial Structures for CSP
CPM 2021   Ranking Bracelets in Polynomial time
BCTCS 2021   Ranking Bracelets in Polynomial time
BCTCS 2020   Multidimensional Necklaces: Enumeration, Generation, Ranking and Unranking
SOFSEM 2020   Crystal Structure Prediction by Vertex Removal in Euclidean Space
BCTCS 2019   Crystal Structure Prediction by Vertex Removal in Euclidean Space