Luke Mathieson

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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)
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)
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)
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)
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)