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Information processing techniques based on sparseness have been actively studied in several disciplines. Among them, a mathematical framework to approximately express a given dataset by a combination of a small number of basis vectors of an…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, informatics, and many other areas. Although there exist several algorithms with acceptable runtimes for certain classes of…
Column-sparse packing problems arise in several contexts in both deterministic and stochastic discrete optimization. We present two unifying ideas, (non-uniform) attenuation and multiple-chance algorithms, to obtain improved approximation…
An elastic-degenerate string is a sequence of $n$ finite sets of strings of total length $N$, introduced to represent a set of related DNA sequences, also known as a pangenome. The ED string matching (EDSM) problem consists in reporting all…
Sparse coding is a class of unsupervised methods for learning a sparse representation of the input data in the form of a linear combination of a dictionary and a sparse code. This learning framework has led to state-of-the-art results in…
This paper presents a new type of genetic algorithm for the set covering problem. It differs from previous evolutionary approaches first because it is an indirect algorithm, i.e. the actual solutions are found by an external decoder…
Motivated by comparative genomics, Chen et al. [9] introduced the Maximum Duo-preservation String Mapping (MDSM) problem in which we are given two strings $s_1$ and $s_2$ from the same alphabet and the goal is to find a mapping $\pi$…
We consider the problem of solving integer programs of the form $\min \{\,c^\intercal x\ \colon\ Ax=b, x\geq 0\}$, where $A$ is a multistage stochastic matrix in the following sense: the primal treedepth of $A$ is bounded by a parameter…
This study develops an algorithm to solve a variation of the Shortest Common Superstring (SCS) problem. There are two modifications to the base SCS problem. First, one string in the set S is allowed to have up to K mistakes, defined as not…
Longest Run Subsequence is a problem introduced recently in the context of the scaffolding phase of genome assembly (Schrinner et al., WABI 2020). The problem asks for a maximum length subsequence of a given string that contains at most one…
Sequence Alignment is the process of aligning biological sequences in order to identify similarities between multiple sequences. In this paper, a Quantum Algorithm for finding the optimal alignment between DNA sequences has been…
An important problem that arises in many engineering applications is the boundary value problem for ordinary differential equations. There have been many computational methods proposed for dealing with this problem. The convergence of the…
In this paper we consider two problems concerning string factorisation. Specifically given a string $w$ and an integer $k$ find a factorisation of $w$ where each factor has length bounded by $k$ and has the minimum (the FmD problem) or the…
Stochastic versions of proximal methods have gained much attention in statistics and machine learning. These algorithms tend to admit simple, scalable forms, and enjoy numerical stability via implicit updates. In this work, we propose and…
Fixed-radius near neighbor search is a fundamental data operation that retrieves all data points within a user-specified distance to a query point. There are efficient algorithms that can provide fast approximate query responses, but they…
In this paper we present a novel non-parametric method of simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. We consider the problem of minimizing…
We start with a review of the pervasiveness of the nearest neighbor search problem and techniques used to solve it along with some experimental results. In the second chapter, we show reductions between two different classes of geo- metric…
Nearest neighbor search is a very active field in machine learning for it appears in many application cases, including classification and object retrieval. In its canonical version, the complexity of the search is linear with both the…
Many separable nonlinear optimization problems can be approximated by their nonlinear objective functions with piecewise linear functions. A natural question arising from applying this approach is how to break the interval of interest into…
Decision-theoretic troubleshooting is one of the areas to which Bayesian networks can be applied. Given a probabilistic model of a malfunctioning man-made device, the task is to construct a repair strategy with minimal expected cost. The…