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Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
Background: We study the sparsification of dynamic programming folding algorithms of RNA structures. Sparsification applies to the mfe-folding of RNA structures and can lead to a significant reduction of time complexity. Results: We analyze…
Algorithms for learning decision trees often include heuristic local-search operations such as (1) adjusting the threshold of a cut or (2) also exchanging the feature of that cut. We study minimizing the number of classification errors by…
We present novel algorithmic techniques to efficiently verify the Kruskal rank of matrices that arise in sparse linear regression, tensor decomposition, and latent variable models. Our unified framework combines randomized hashing…
In this paper, sparsification techniques aided online prediction algorithms in a reproducing kernel Hilbert space are studied for nonstationary time series. The online prediction algorithms as usual consist of the selection of kernel…
In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…
Benchmark problems are an important tool for gaining understanding of optimization algorithms. Since algorithms often aim to perform well on benchmarks, biases in benchmark design provide misleading insights. In single-objective…
We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…
The current landscape of balanced graph partitioning is divided into high-quality but expensive multilevel algorithms and cheaper approaches with linear running time, such as single-level algorithms and streaming algorithms. We demonstrate…
Deep declarative networks and other recent related works have shown how to differentiate the solution map of a (continuous) parametrized optimization problem, opening up the possibility of embedding mathematical optimization problems into…
The problem of scheduling with testing in the framework of explorable uncertainty models environments where some preliminary action can influence the duration of a task. In the model, each job has an unknown processing time that can be…
We introduce a generic framework for solving linear programs (LPs) with many constraints $(n \gg d)$ via adaptive sparsification. Our approach provides a principled generalization of the techniques of [Assadi '23] from matching problems to…
This paper presents an acceleration framework for packing linear programming problems where the amount of data available is limited, i.e., where the number of constraints m is small compared to the variable dimension n. The framework can be…
Sparse Principal Component Analysis (Sparse PCA) is a pivotal tool in data analysis and dimensionality reduction. However, Sparse PCA is a challenging problem in both theory and practice: it is known to be NP-hard and current exact methods…
We present linear-space data structures for several frequency queries on trees, namely: path mode, path least frequent element, and path $\alpha$-minority queries. We present the first linear-space data structures, requiring $O(n…
Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch &…
We study a structured linear program (LP) that emerges in the need of ranking candidates or items in personalized recommender systems. Since the candidate set is only known in real time, the LP also needs to be formed and solved in real…
In this paper, we obtain improved running times for regression and top eigenvector computation for numerically sparse matrices. Given a data matrix $A \in \mathbb{R}^{n \times d}$ where every row $a \in \mathbb{R}^d$ has $\|a\|_2^2 \leq L$…
Entity Resolution (ER) is typically implemented as a batch task that processes all available data before identifying duplicate records. However, applications with time or computational constraints, e.g., those running in the cloud, require…
In this paper, we generalize Spencer's hyperbolic cosine algorithm to the matrix-valued setting. We apply the proposed algorithm to several problems by analyzing its computational efficiency under two special cases of matrices; one in which…