Related papers: Euclidean correlations in combinatorial optimizati…
We study the classical 1D Heisenberg spin glasses. Based on the Hamilton equations we obtained the system of recurrence equations which allows to perform node-by-node calculations of a spin-chain. It is shown that calculations from first…
The Travelling Salesman Problem (TSP) is a classical combinatorial optimisation problem. Deep learning has been successfully extended to meta-learning, where previous solving efforts assist in learning how to optimise future optimisation…
In recent years, quantum computing has drawn significant interest within the field of high-energy physics. We explore the potential of quantum algorithms to resolve the combinatorial problems in particle physics experiments. As a concrete…
Analog quantum computing with Rydberg atoms is seen as an avenue to solve hard graph optimization problems, because they naturally encode the Maximum Independent Set (MIS) problem on Unit-Disk (UD) graphs, a problem that admits rather…
Combinatorial optimization is the field devoted to the study and practice of algorithms that solve NP-hard problems. As Machine Learning (ML) and deep learning have popularized, several research groups have started to use ML to solve…
Combinatorial optimization problems are ubiquitous in industrial applications. However, finding optimal or close-to-optimal solutions can often be extremely hard. Because some of these problems can be mapped to the ground-state search of…
We solve crossing equations analytically in the deep Euclidean regime. Large scaling dimension $\Delta$ tails of the weighted spectral density of primary operators of given spin in one channel are matched to the Euclidean OPE data in the…
One of the challenges in optimization of high dimensional problems is finding appropriate solutions in a way that are as close as possible to the global optima. In this regard, one of the most common phenomena that occurs is the curse of…
I give a very brief non-technical introduction to the intersection of the fields of spin systems and computational complexity. The focus is on spin glasses and their relationship to NP-complete problems.
We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in $\mathbb{R}^d$ where the edge cost between two points is given by a $p$-th power of their Euclidean distance.…
Mathematical Selection is a method in which we select a particular choice from a set of such. It have always been an interesting field of study for mathematicians. Accordingly, Combinatorial Optimization is a sub field of this domain of…
Krentel [J. Comput. System. Sci., 36, pp.490--509] presented a framework for an NP optimization problem that searches an optimal value among exponentially-many outcomes of polynomial-time computations. This paper expands his framework to a…
Optimally selecting a subset of targets from a larger catalog is a common problem in astronomy and cosmology. A specific example is the selection of targets from an imaging survey for multi-object spectrographic follow-up. We present a new…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
Uncertainty is fundamental in modern power systems, where renewable generation and fluctuating demand make stochastic optimization indispensable. The chance constrained unit commitment problem (UCP) captures this uncertainty but rapidly…
Clustering is a fundamental task in data science that aims to group data based on their similarities. However, defining similarity is often ambiguous, making it challenging to determine the most appropriate objective function for a given…
Quadratic programming (QP) is a common and important constrained optimization problem. Here, we derive a surprising duality between constrained optimization with inequality constraints -- of which QP is a special case -- and consumer…
We propose a new approach for the study of the quadratic stochastic Euclidean bipartite matching problem between two sets of $N$ points each, $N\gg 1$. The points are supposed independently randomly generated on a domain…
Probabilistic analysis for metric optimization problems has mostly been conducted on random Euclidean instances, but little is known about metric instances drawn from distributions other than the Euclidean. This motivates our study of…
We present herein a new approach based on the simultaneous application of the deep learning and statistical physics methods to solve the combinatorial optimization problems. The recent modern advanced techniques, such as an artificial…