相关论文: Analysis of the Harmonic Function Used in Bin-Pack…

Since Voiculescu introduced his bi-free probability theory in 2013, the major development of the theory has been on its combinatorial side; in particular, on the combinatorics of bi-free cumulants and its application to the bi-free…

Since the Bin Packing Problem (BPP) is one of the main NP-hard problems, a lot of approximation algorithms have been suggested for it. It has been proven that the best algorithm for BPP has the approximation ratio of 3/2 and the time order…

We study a variant of online bin packing, called colorful bin packing. In this problem, items that are presented one by one are to be packed into bins of size 1. Each item i has a size s_i \in [0,1] and a color c_i \in C, where C is a set…

We study the complexity of sampling, rounding, and integrating arbitrary logconcave functions. Our new approach provides the first complexity improvements in nearly two decades for general logconcave functions for all three problems, and…

A generalized harmonic map equation is presented based on the proposed action functional in the Weyl space (PLA, 135, 315, 1989).

During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…

Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the…

Given a list of N numbers, the maximum can be computed in N iterations. During these N iterations, the maximum gets updated on average as many times as the Nth harmonic number. We first use this fact to approximate the Nth harmonic number…

The Bin Packing Problem is one of the most important Combinatorial Optimization problems in optimization and has a lot of real-world applications. Many approximation algorithms have been presented for this problem because of its NP-hard…

This paper presents an evaluation framework for assessing Large Language Models' (LLMs) capabilities in combinatorial optimization, specifically addressing the 2D bin-packing problem. We introduce a systematic methodology that combines LLMs…

In the Colored Bin Packing problem a sequence of items of sizes up to $1$ arrives to be packed into bins of unit capacity. Each item has one of $c\geq 2$ colors and an additional constraint is that we cannot pack two items of the same color…

The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.

These notes present a first graduate course in harmonic analysis. The first part emphasizes Fourier series, since so many aspects of harmonic analysis arise already in that classical context. The Hilbert transform is treated on the circle,…

We address the problem of finding harmonic colors, this problem has many applications, from fashion to industrial design. In order to solve this problem we consider that colors follow normal distributions in tone (chroma and lightness) and…

The Bin Packing Problem involves efficiently packing items into a limited number of bins without exceeding their capacity. In this paper, we try to answer a specific question in this field. Mathematically the combinatorial optimization…

We present the first potential function for pairing heaps with linear range. This implies that the runtime of a short sequence of operations is faster than previously known. It is also simpler than the only other potential function known to…

HarmonicBalance.jl is a publicly available Julia package designed to simplify and solve systems of periodic time-dependent nonlinear ordinary differential equations. Time dependence of the system parameters is treated with the harmonic…

Current image harmonization methods consider the entire background as the guidance for harmonization. However, this may limit the capability for user to choose any specific object/person in the background to guide the harmonization. To…

In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or…

The Bin Packing Problem is a classic problem with wide industrial applicability. In fact, the efficient packing of items into bins is one of the toughest challenges in many logistic corporations and is a critical issue for reducing storage…