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The contraction cost of a tensor network depends on the contraction order. However, the optimal contraction ordering problem is known to be NP-hard. We show that the linear contraction ordering problem for tree tensor networks admits a…
The era of huge data necessitates highly efficient machine learning algorithms. Many common machine learning algorithms, however, rely on computationally intensive subroutines that are prohibitively expensive on large datasets. Oftentimes,…
Sparsity-based methods are widely used in machine learning, statistics, and signal processing. There is now a rich class of structured sparsity approaches that expand the modeling power of the sparsity paradigm and incorporate constraints…
In time series analysis, when fitting an autoregressive model, one must solve a Toeplitz ordinary least squares problem numerous times to find an appropriate model, which can severely affect computational times with large data sets. Two…
One of the most fundamental method for comparing two given strings $A$ and $B$ is the longest common subsequence (LCS), where the task is to find (the length) of an LCS of $A$ and $B$. In this paper, we deal with the STR-IC-LCS problem…
The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners,…
Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
Hierarchical clustering is a critical task in numerous domains. Many approaches are based on heuristics and the properties of the resulting clusterings are studied post hoc. However, in several applications, there is a natural cost function…
Sinkhorn algorithm is the de-facto standard approximation algorithm for optimal transport, which has been applied to a variety of applications, including image processing and natural language processing. In theory, the proof of its…
Since a few years there is an increasing interest in minimizing the energy consumption of computing systems. However in a shared computing system, users want to optimize their experienced quality of service, at the price of a high energy…
We consider the problem of allocating multiple heterogeneous resources geographically and over time to meet demands that require some subset of the available resource types simultaneously at a specified time, location, and duration. The…
We formulate a strong equivalence between machine learning, artificial intelligence methods and the formulation of statistical data assimilation as used widely in physical and biological sciences. The correspondence is that layer number in…
Evaluating solutions to optimization problems is arguably the most important step for heuristic algorithms, as it is used to guide the algorithms towards the optimal solution in the solution search space. Research has shown evaluation…
We consider an incremental approximation method for solving variational problems in infinite-dimensional Hilbert spaces, where in each step a randomly and independently selected subproblem from an infinite collection of subproblems is…
Despite recent advances in subquadratic attention mechanisms or state-space models, processing long token sequences still imposes significant computational requirements. Token merging has emerged as a solution to increase computational…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
In high-dimensional generalized linear models, it is crucial to identify a sparse model that adequately accounts for response variation. Although the best subset section has been widely regarded as the Holy Grail of problems of this type,…
In this paper, we introduce some new hybrid algorithms for finding a solution of a system of equilibrium problems. In these algorithms, by constructing specially cutting-halfspaces, we avoid using the extra-steps as in the extragradient…
Sequence comparison is a widely used computational technique in modern molecular biology. In spite of the frequent use of sequence comparisons the important problem of assigning statistical significance to a given degree of similarity is…
Algebraic multigrid (AMG) is one of the most widely used solution techniques for linear systems of equations arising from discretized partial differential equations. The popularity of AMG stems from its potential to solve linear systems in…