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- Luke Mathieson, Stefan Szeider
- J. Comput. Syst. Sci.
- 2012

We study a wide class of graph editing problems that ask whether a given graph can be modified to satisfy certain degree constraints, using a limited number of vertex deletions, edge deletions, or edge additions. The problems generalize several well-studied problems such as the General Factor Problem and the Regular Subgraph Problem. We classify the… (More)

- Luke Mathieson, Elena Prieto, Peter Shaw
- IWPEC
- 2004

The problem of packing k edge-disjoint triangles in a graph has been thoroughly studied both in the classical complexity and the approximation fields and it has a wide range of applications in many areas, especially computational biology [BP96]. In this paper we present an analysis of the problem from a parameterized complexity viewpoint. We describe a… (More)

- Fabrizio Frati, Serge Gaspers, Joachim Gudmundsson, Luke Mathieson
- Algorithmica
- 2013

We study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph. Our main result is an FPT $$4$$ 4 -approximation algorithm for the problem.

Novel analytical techniques have dramatically enhanced our understanding of many application domains including biological networks inferred from gene expression studies. However, there are clear computational challenges associated to the large datasets generated from these studies. The algorithmic solution of some NP-hard combinatorial optimization problems… (More)

- Luke Mathieson
- Theor. Comput. Sci.
- 2010

- Luke Mathieson
- 2009

- Luke Mathieson, Stefan Szeider
- COCOA
- 2008

We study the parameterized complexity of the following problem: is it possible to make a given graph r-regular by applying at most k elementary editing operations; the operations are vertex deletion, edge deletion, and edge addition. We also consider more general annotated variants of this problem, where vertices and edges are assigned an integer cost and… (More)

- Luke Mathieson
- Theor. Comput. Sci.
- 2017

Graph editing problems offer an interesting perspective on suband supergraph identification problems for a large variety of target properties. They have also attracted significant attention in recent years, particularly in the area of parameterized complexity as the problems have rich parameter ecologies. In this paper we examine generalisations of the… (More)

- Sergei Konyagin, Florian Luca, Bernard Mans, Luke Mathieson, Igor E. Shparlinski
- J. Comb. Theory, Ser. B
- 2016

Given a function f in a finite field IFq we define the functional graph of f as a directed graph on q nodes labelled by elements of IFq where there is an edge from u to v if and only if f(u) = v. We obtain some theoretic estimates on the number of non-isomorphic graphs generated by all polynomials of a given degree. We then develop an algorithm to test the… (More)

- Ahmed Shamsul Arefin, Luke Mathieson, Daniel Johnstone, Regina Berretta, Pablo Moscato
- PloS one
- 2012

BACKGROUND
One primary goal of transcriptomic studies is identifying gene expression patterns correlating with disease progression. This is usually achieved by considering transcripts that independently pass an arbitrary threshold (e.g. p<0.05). In diseases involving severe perturbations of multiple molecular systems, such as Alzheimer's disease (AD), this… (More)