Related papers: A Faster FPTAS for the Subset-Sums Ratio Problem

We present a new algorithm that achieves a $\frac{7}{9}$-approximation for the maximin share (MMS) allocation of indivisible goods under additive valuations, improving the current best ratio of $\frac{10}{13}$ (Heidari et al., SODA 2026).…

Many statistical methods require solutions to optimization problems. When the global solution is hard to attain, statisticians always use the better if there are two solutions for chosen, where the word "better" is understood in the sense…

Sparse recovery and subset selection are fundamental problems in varied communities, including signal processing, statistics and machine learning. Herein, we focus on an important greedy algorithm for these problems: Backward Stepwise…

Sum of squares (SOS) optimization is a powerful technique for solving problems where the positivity of a polynomials must be enforced. The common approach to solve an SOS problem is by relaxation to a Semidefinite Program (SDP). The main…

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The two-stage stochastic unit commitment problem has become an important tool to support decision-making under uncertainty in power systems. Representing the uncertainty by a large number of scenarios guarantees accurate results but…

Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets $n$ be the number of constraints and $d$ be the number of variables, with…

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Sparse Representation (SR) techniques encode the test samples into a sparse linear combination of all training samples and then classify the test samples into the class with the minimum residual. The classification of SR techniques depends…

An efficient hardware implementation for Simultaneous Localization and Mapping (SLAM) methods is of necessity for mobile autonomous robots with limited computational resources. In this paper, we propose a resource-efficient FPGA…

I present two new methods for exactly summing a set of floating-point numbers, and then correctly rounding to the nearest floating-point number. Higher accuracy than simple summation (rounding after each addition) is important in many…

Here several perfect simulation algorithms are brought under a single framework, and shown to derive from the same probabilistic result, called here the Fundamental Theorem of Perfect Simulation (FTPS). An exact simulation algorithm has…

We present a new space-efficient approach, (SparseDTW), to compute the Dynamic Time Warping (DTW) distance between two time series that always yields the optimal result. This is in contrast to other known approaches which typically…

Extracting a small subset of representative tuples from a large database is an important task in multi-criteria decision making. The regret-minimizing set (RMS) problem is recently proposed for representative discovery from databases.…

The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis -…

This paper studies the problem of Simultaneous Sparse Approximation (SSA). This problem arises in many applications which work with multiple signals maintaining some degree of dependency such as radar and sensor networks. In this paper, we…

We give the first deterministic fully polynomial-time approximation scheme (FPTAS) for computing the partition function of a two-state spin system on an arbitrary graph, when the parameters of the system satisfy the uniqueness condition on…

We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or…

We provide faster algorithms for the problem of Gaussian summation, which occurs in many machine learning methods. We develop two new extensions - an O(Dp) Taylor expansion for the Gaussian kernel with rigorous error bounds and a new error…

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