Towards Effective Exact Algorithms for the Maximum Balanced Biclique Problem

The Maximum Balanced Biclique Problem (MBBP) is a prominent model with numerous applications. Yet, the problem is NP-hard and thus computationally challenging. We propose novel ideas for designing effective exact algorithms for MBBP. Firstly, we introduce an Upper Bound Propagation procedure to pre-compute an upper bound involving each vertex. Then we extend an existing branch-and-bound algorithm by integrating the pre-computed upper bounds. We also present a set of new valid inequalities induced from the upper bounds to tighten an existing mathematical formulation for MBBP. Lastly, we investigate another exact algorithm scheme which enumerates a subset of balanced bicliques based on our upper bounds. Experiments show that compared to existing approaches, the proposed algorithms and formulations are more efficient in solving a set of random graphs and large real-life instances

Multipartite Graph Algorithms for the Analysis of Heterogeneous Data

The explosive growth in the rate of data generation in recent years threatens to outpace the growth in computer power, motivating the need for new, scalable algorithms and big data analytic techniques. No field may be more emblematic of this data deluge than the life sciences, where technologies such as high-throughput mRNA arrays and next generation genome sequencing are routinely used to generate datasets of extreme scale. Data from experiments in genomics, transcriptomics, metabolomics and proteomics are continuously being added to existing repositories. A goal of exploratory analysis of such omics data is to illuminate the functions and relationships of biomolecules within an organism. This dissertation describes the design, implementation and application of graph algorithms, with the goal of seeking dense structure in data derived from omics experiments in order to detect latent associations between often heterogeneous entities, such as genes, diseases and phenotypes. Exact combinatorial solutions are developed and implemented, rather than relying on approximations or heuristics, even when problems are exceedingly large and/or difficult. Datasets on which the algorithms are applied include time series transcriptomic data from an experiment on the developing mouse cerebellum, gene expression data measuring acute ethanol response in the prefrontal cortex, and the analysis of a predicted protein-protein interaction network. A bipartite graph model is used to integrate heterogeneous data types, such as genes with phenotypes and microbes with mouse strains. The techniques are then extended to a multipartite algorithm to enumerate dense substructure in multipartite graphs, constructed using data from three or more heterogeneous sources, with applications to functional genomics. Several new theoretical results are given regarding multipartite graphs and the multipartite enumeration algorithm. In all cases, practical implementations are demonstrated to expand the frontier of computational feasibility

A survey of fault-tolerance algorithms for reconfigurable nano-crossbar arrays

ACM Comput. Surv. Volume 50, issue 6 (November 2017)Nano-crossbar arrays have emerged as a promising and viable technology to improve computing performance of electronic circuits beyond the limits of current CMOS. Arrays offer both structural efficiency with reconfiguration and prospective capability of integration with different technologies. However, certain problems need to be addressed, and the most important one is the prevailing occurrence of faults. Considering fault rate projections as high as 20% that is much higher than those of CMOS, it is fair to expect sophisticated fault-tolerance methods. The focus of this survey article is the assessment and evaluation of these methods and related algorithms applied in logic mapping and configuration processes. As a start, we concisely explain reconfigurable nano-crossbar arrays with their fault characteristics and models. Following that, we demonstrate configuration techniques of the arrays in the presence of permanent faults and elaborate on two main fault-tolerance methodologies, namely defect-unaware and defect-aware approaches, with a short review on advantages and disadvantages. For both methodologies, we present detailed experimental results of related algorithms regarding their strengths and weaknesses with a comprehensive yield, success rate and runtime analysis. Next, we overview fault-tolerance approaches for transient faults. As a conclusion, we overview the proposed algorithms with future directions and upcoming challenges.This work is supported by the EU-H2020-RISE project NANOxCOMP no 691178 and the TUBITAK-Career project no 113E760

Multi-biclustering solutions for classification and prediction problems

2009 - 20101The search for similarities in large data sets has a relevant role in many scientific fields. It permits to classify several types of data without an explicit information about them. Unfortunately, the experimental data contains noise and errors, and therefore the main task of mathematicians is to find algorithms that permit to analyze this data with maximal precision. In many cases researchers use methodologies such as clustering to classify data with respect to the patterns or conditions. But in the last few years new analysis tool such as biclustering was proposed and applied to many specific problems. My choice of biclustering methods is motivated by the accuracy obtained in the results and the possibility to find not only rows or columns that provide a dataset partition but also rows and columns together. In this work, two new biclustering algorithms, the Combinatorial Biclustering Algorithm (CBA) and an improvement of the Possibilistic Biclustering Algorithm, called Biclustering by resampling, are presented. The first algorithm (that I call Combinatorial) is based on the direct definition of bicluster, that makes it clear and very easy to understand. My algorithm permits to control the error of biclusters in each step, specifying the accepted value of the error and defining the dimensions of the desired biclusters from the beginning. The comparison with other known biclustering algorithms is shown. The second algorithm is an improvement of the Possibilistic Biclustering Algorithm (PBC). The PBC algorithm, proposed by M. Filippone et al., is based on the Possibilistic Clustering paradigm, and finds one bicluster at a time, assigning a membership to the bicluster for each gene and for each condition. PBC uses an objective function that maximizes a bicluster cardinality and minimizes a residual error. The biclustering problem is faced as the optimization of a proper functional. This algorithm obtains a fast convergence and good quality of the solutions. Unfortunately, PBC finds only one bicluster at a time. I propose an improved PBC algorithm based on data resampling, specifically Bootstrap aggregation, and Genetics algorithms. In such a way I can find all the possible biclusters together and include overlapped solutions. I apply the algorithm to a synthetic data and to the Yeast dataset and compare it with the original PBC method. [edited by the author]IX n.s

Maximizing lifetime of range-adjustable wireless sensor networks: a neighborhood-based estimation of distribution algorithm

Sensor activity scheduling is critical for prolonging the lifetime of wireless sensor networks (WSNs). However, most existing methods assume sensors to have one fixed sensing range. Prevalence of sensors with adjustable sensing ranges posts two new challenges to the topic: 1) expanded search space, due to the rise in the number of possible activation modes and 2) more complex energy allocation, as the sensors differ in the energy consumption rate when using different sensing ranges. These two challenges make it hard to directly solve the lifetime maximization problem of WSNs with range-adjustable sensors (LM-RASs). This article proposes a neighborhood-based estimation of distribution algorithm (NEDA) to address it in a recursive manner. In NEDA, each individual represents a coverage scheme in which the sensors are selectively activated to monitor all the targets. A linear programming (LP) model is built to assign activation time to the schemes in the population so that their sum, the network lifetime, can be maximized conditioned on the current population. Using the activation time derived from LP as individual fitness, the NEDA is driven to seek coverage schemes promising for prolonging the network lifetime. The network lifetime is thus optimized by repeating the steps of the coverage scheme evolution and LP model solving. To encourage the search for diverse coverage schemes, a neighborhood sampling strategy is introduced. Besides, a heuristic repair strategy is designed to fine-tune the existing schemes for further improving the search efficiency. Experimental results on WSNs of different scales show that NEDA outperforms state-of-the-art approaches. It is also expected that NEDA can serve as a potential framework for solving other flexible LP problems that share the same structure with LM-RAS

Multi-layered model of individual HIV infection progression and mechanisms of phenotypical expression

Cite as: Perrin, Dimitri (2008) Multi-layered model of individual HIV infection progression and mechanisms of phenotypical expression. PhD thesis, Dublin City University

Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization

Many real-life decision problems are discrete in nature. To solve such problems as mathematical optimization problems, integrality constraints are commonly incorporated in the model to reflect the choice of finitely many alternatives. At the same time, it is known that semidefinite programming is very suitable for obtaining strong relaxations of combinatorial optimization problems. In this dissertation, we study the interplay between semidefinite programming and integrality, where a special focus is put on the use of cutting-plane methods. Although the notions of integrality and cutting planes are well-studied in linear programming, integer semidefinite programs (ISDPs) are considered only recently. We show that manycombinatorial optimization problems can be modeled as ISDPs. Several theoretical concepts, such as the Chvátal-Gomory closure, total dual integrality and integer Lagrangian duality, are studied for the case of integer semidefinite programming. On the practical side, we introduce an improved branch-and-cut approach for ISDPs and a cutting-plane augmented Lagrangian method for solving semidefinite programs with a large number of cutting planes. Throughout the thesis, we apply our results to a wide range of combinatorial optimization problems, among which the quadratic cycle cover problem, the quadratic traveling salesman problem and the graph partition problem. Our approaches lead to novel, strong and efficient solution strategies for these problems, with the potential to be extended to other problem classes

Semantic Biclustering

Tato disertační práce se zaměřuje na problém hledání interpretovatelných a prediktivních vzorů, které jsou vyjádřeny formou dvojshluků, se specializací na biologická data. Prezentované metody jsou souhrnně označovány jako sémantické dvojshlukování, jedná se o podobor dolování dat. Termín sémantické dvojshlukování je použit z toho důvodu, že zohledňuje proces hledání koherentních podmnožin řádků a sloupců, tedy dvojshluků, v 2-dimensionální binární matici a zárove ň bere také v potaz sémantický význam prvků v těchto dvojshlucích. Ačkoliv byla práce motivována biologicky orientovanými daty, vyvinuté algoritmy jsou obecně aplikovatelné v jakémkoli jiném výzkumném oboru. Je nutné pouze dodržet požadavek na formát vstupních dat. Disertační práce představuje dva originální a v tomto ohledu i základní přístupy pro hledání sémantických dvojshluků, jako je Bicluster enrichment analysis a Rule a tree learning. Jelikož tyto metody nevyužívají vlastní hierarchické uspořádání termů v daných ontologiích, obecně je běh těchto algoritmů dlouhý čin může docházet k indukci hypotéz s redundantními termy. Z toho důvodu byl vytvořen nový operátor zjemnění. Tento operátor byl včleněn do dobře známého algoritmu CN2, kde zavádí dvě redukční procedury: Redundant Generalization a Redundant Non-potential. Obě procedury pomáhají dramaticky prořezat prohledávaný prostor pravidel a tím umožňují urychlit proces indukce pravidel v porovnání s tradičním operátorem zjemnění tak, jak je původně prezentován v CN2. Celý algoritmus spolu s redukčními metodami je publikován ve formě R balííčku, který jsme nazvali sem1R. Abychom ukázali i možnost praktického užití metody sémantického dvojshlukování na reálných biologických problémech, v disertační práci dále popisujeme a specificky upravujeme algoritmus sem1R pro dv+ úlohy. Zaprvé, studujeme praktickou aplikaci algoritmu sem1R v analýze E-3 ubikvitin ligázy v trávicí soustavě s ohledem na potenciál regenerace tkáně. Zadruhé, kromě objevování dvojshluků v dat ech genové exprese, adaptujeme algoritmus sem1R pro hledání potenciálne patogenních genetických variant v kohortě pacientů.This thesis focuses on the problem of finding interpretable and predic tive patterns, which are expressed in the form of biclusters, with an orientation to biological data. The presented methods are collectively called semantic biclustering, as a subfield of data mining. The term semantic biclustering is used here because it reflects both a process of finding coherent subsets of rows and columns in a 2-dimensional binary matrix and simultaneously takes into account a mutual semantic meaning of elements in such biclusters. In spite of focusing on applications of algorithms in biological data, the developed algorithms are generally applicable to any other research field, there are only limitations on the format of the input data. The thesis introduces two novel, and in that context basic, approaches for finding semantic biclusters, as Bicluster enrichment analysis and Rule and tree learning. Since these methods do not exploit the native hierarchical order of terms of input ontologies, the run-time of algorithms is relatively long in general or an induced hypothesis might have terms that are redundant. For this reason, a new refinement operator has been invented. The refinement operator was incorporated into the well-known CN2 algorithm and uses two reduction procedures: Redundant Generalization and Redundant Non-potential, both of which help to dramatically prune the rule space and consequently, speed-up the entire process of rule induction in comparison with the traditional refinement operator as is presented in CN2. The reduction procedures were published as an R package that we called sem1R. To show a possible practical usage of semantic biclustering in real biological problems, the thesis also describes and specifically adapts the algorithm for two real biological problems. Firstly, we studied a practical application of sem1R algorithm in an analysis of E-3 ubiquitin ligase in the gastrointestinal tract with respect to tissue regeneration potential. Secondly, besides discovering biclusters in gene expression data, we adapted the sem1R algorithm for a different task, concretely for finding potentially pathogenic genetic variants in a cohort of patients