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Kloks, Kratsch, and Spinrad showed how treewidth and minimum-fill, NP-hard combinatorial optimization problems related to minimal triangulations, are broken into subproblems by block subgraphs defined by minimal separators. These ideas were…
Phylogenetic trees and networks are leaf-labelled graphs that are used to describe evolutionary histories of species. The Tree Containment problem asks whether a given phylogenetic tree is embedded in a given phylogenetic network. Given a…
Given an edge-colored graph, the Maximum Rainbow Matching problem asks for a maximum-cardinality matching of the graph that contains at most one edge from each color. We provide the following complexity dichotomy for this problem based on…
A definitive diagnosis of a brain tumour is essential for enhancing treatment success and patient survival. However, it is difficult to manually evaluate multiple magnetic resonance imaging (MRI) images generated in a clinic. Therefore,…
This research proposes a very lightweight model "Fibonacci-Net" along with a novel pooling technique, for automatic brain tumor classification from imbalanced Magnetic Resonance Imaging (MRI) datasets. Automatic brain tumor detection from…
Single individual haplotyping is an NP-hard problem that emerges when attempting to reconstruct an organism's inherited genetic variations using data typically generated by high-throughput DNA sequencing platforms. Genomes of diploid…
Automated brain tumor detection is becoming a highly considerable medical diagnosis research. In recent medical diagnoses, detection and classification are highly considered to employ machine learning and deep learning techniques.…
We study the problem of recovering an incomplete $m\times n$ matrix of rank $r$ with columns arriving online over time. This is known as the problem of life-long matrix completion, and is widely applied to recommendation system, computer…
Clusters of genes that have evolved by repeated segmental duplication present difficult challenges throughout genomic analysis, from sequence assembly to functional analysis. Improved understanding of these clusters is of utmost importance,…
Heterogeneity in the cell population of cancer tissues poses many challenges in cancer diagnosis and treatment. Studying the heterogeneity in cell populations from gene expression measurement data in the context of cancer research is a…
This paper considers the problem of completing a rating matrix based on sub-sampled matrix entries as well as observed social graphs and hypergraphs. We show that there exists a \emph{sharp threshold} on the sample probability for the task…
We study complexity of rearrangement problems in the generalized breakpoint model and settle several open questions. The model was introduced by Tannier et al. (2009) who showed that the median problem is solvable in polynomial time in the…
We consider the NP-hard Tree Containment problem that has important applications in phylogenetics. The problem asks if a given leaf-labeled network contains a subdivision of a given leaf-labeled tree. We develop a fast algorithm for the…
Hierarchical clustering is a fundamental task often used to discover meaningful structures in data, such as phylogenetic trees, taxonomies of concepts, subtypes of cancer, and cascades of particle decays in particle physics. Typically…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
Recent advances in cancer research largely rely on new developments in microscopic or molecular profiling techniques offering high level of detail with respect to either spatial or molecular features, but usually not both. Here, we present…
In this paper we present a collection of results pertaining to haplotyping. The first set of results concerns the combinatorial problem of reconstructing haplotypes from incomplete and/or imperfectly sequenced haplotype data. More…
Understanding genetic variation, e.g., through mutations, in organisms is crucial to unravel their effects on the environment and human health. A fundamental characterization can be obtained by solving the haplotype assembly problem, which…
We introduce the strongly NP-complete pagination problem, an extension of BIN PACKING where packing together two items may make them occupy less volume than the sum of their individual sizes. To achieve this property, an item is defined as…
Phylogenetic networks are often constructed by merging multiple conflicting phylogenetic signals into a directed acyclic graph. It is interesting to explore whether a network constructed in this way induces biologically-relevant…