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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 Sub-graph Problem. We classify the… (More)

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 al-gorithmic solution of some NP-hard combinatorial optimization… (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)

- 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)

- 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.

- Luke Mathieson, Stefan Szeider
- CATS
- 2008

We study variants and generalizations of the problem of finding an r-regular subgraph (where r ≥ 3) in a given graph by deleting at most k vertices. Moser and Thilikos (2006) have shown that the problem is fixed-parameter tractable (FPT) if parameterized by (k, r). They asked whether the problem remains fixed-parameter tractable if parameterized by k alone.… (More)

- Romeo Rizzi, Pritha Mahata, Luke Mathieson, Pablo Moscato
- PloS one
- 2010

Clustering, particularly hierarchical clustering, is an important method for understanding and analysing data across a wide variety of knowledge domains with notable utility in systems where the data can be classified in an evolutionary context. This paper introduces a new hierarchical clustering problem defined by a novel objective function we call the… (More)

- Bernard Mans, Luke Mathieson
- COCOON
- 2013

Dynamic graph theory is a novel, growing area that deals with graphs that change over time and is of great utility in modelling modern wireless, mobile and dynamic environments. As a graph evolves, possibly arbitrarily, it is challenging to identify the graph properties that can be preserved over time and understand their respective computability. In this… (More)

The data mining inspired problem of finding the critical , and most useful features to be used to classify a data set, and construct rules to predict the class of future examples is an interesting and important problem. It is also one of the most useful problems with applications in many areas such as microarray analysis , genomics, proteomics, pattern… (More)

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