Related papers: A Faster FPTAS for the Subset-Sums Ratio Problem
Fine-tuning Large Language Models (LLMs) on specific datasets is a common practice to improve performance on target tasks. However, this performance gain often leads to overfitting, where the model becomes too specialized in either the task…
This paper considers the arbitrary-proportional finite-set-partitioning problem which involves partitioning a finite set into multiple subsets with respect to arbitrary nonnegative proportions. This is the core art of many fundamental…
The least trimmed squares (LTS) is a reasonable formulation of robust regression whereas it suffers from high computational cost due to the nonconvexity and nonsmoothness of its objective function. The most frequently used FAST-LTS…
The success of deep learning hinges on enormous data and large models, which require labor-intensive annotations and heavy computation costs. Subset selection is a fundamental problem that can play a key role in identifying smaller portions…
We consider the sparse optimization problem with nonlinear constraints and an objective function, which is given by the sum of a general smooth mapping and an additional term defined by the $ \ell_0 $-quasi-norm. This term is used to obtain…
We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes.…
Fairness of decision-making algorithms is an increasingly important issue. In this paper, we focus on spectral clustering with group fairness constraints, where every demographic group is represented in each cluster proportionally as in the…
The dramatic growth of big datasets presents a new challenge to data storage and analysis. Data reduction, or subsampling, that extracts useful information from datasets is a crucial step in big data analysis. We propose an orthogonal…
In computational and applied statistics, it is of great interest to get fast and accurate calculation for the distributions of the quadratic forms of Gaussian random variables. This paper presents a novel approximation strategy that…
An unconstrained nonlinear binary optimization problem of selecting a maximum expected value subset of items is considered. Each item is associated with a profit and probability. Each of the items succeeds or fails independently with the…
The convergence rate is analyzed for the SpaSRA algorithm (Sparse Reconstruction by Separable Approximation) for minimizing a sum $f (\m{x}) + \psi (\m{x})$ where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that…
We study real-time routing policies in smart transit systems, where the platform has a combination of cars and high-capacity vehicles (e.g., buses or shuttles) and seeks to serve a set of incoming trip requests. The platform can use its…
We propose a novel approach for the development, analysis, and verification of reductions between NP-complete problems. This method uses the URSA system, a SAT-based constraint solver and incorporates features that distinguish it from…
We introduce fast randomized algorithms for solving semidefinite programming (SDP) relaxations of the partial permutation synchronization (PPS) problem, a core task in multi-image matching with significant relevance to 3D reconstruction.…
When minimizing the sum of a convex and a strongly convex function, or when finding the zero of the sum of a monotone operator and a strongly monotone operator, Chambolle and Pock (2010) and Davis and Yin (2015) proposed accelerated…
In the field of algorithmic analysis, one of the more well-known exercises is the subset sum problem. That is, given a set of integers, determine whether one or more integers in the set can sum to a target value. Aside from the brute-force…
The problem of biclustering consists of the simultaneous clustering of rows and columns of a matrix such that each of the submatrices induced by a pair of row and column clusters is as uniform as possible. In this paper we approximate the…
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it,…
Subset-Sum is an NP-complete problem where one must decide if a multiset of $n$ integers contains a subset whose elements sum to a target value $m$. The best-known classical and quantum algorithms run in time $\tilde{O}(2^{n/2})$ and…
In this paper, we propose a novel algorithm for analysis-based sparsity reconstruction. It can solve the generalized problem by structured sparsity regularization with an orthogonal basis and total variation regularization. The proposed…