相关论文: A Light-Based Device for Solving the Hamiltonian P…

To solve many problems on graphs, graph traversals are used, the usual variants of which are the depth-first search and the breadth-first search. Implementing a graph traversal we consequently reach all vertices of the graph that belong to…

Graph embedding algorithms are used to efficiently represent (encode) a graph in a low-dimensional continuous vector space that preserves the most important properties of the graph. One aspect that is often overlooked is whether the graph…

The aim of this paper is to present an algorithm which gives all the possible paths that start from a specific node to another of a weighted multi-graph. This algorithm is intended to be applied for the direct topological method.

The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…

In graph theory, the longest path problem is the problem of finding a simple path of maximum length in a given graph. For some small classes of graphs, the problem can be solved in polynomial time [2, 4], but it remains NP-hard on general…

The monography considers the problem of constructing a Hamiltonian cycle in a complete graph. A rule for constructing a Hamiltonian cycle based on isometric cycles of a graph is established. An algorithm for constructing a Hamiltonian cycle…

Differentiable rendering methods promise the ability to optimize various parameters of 3d scenes to achieve a desired result. However, lighting design has so far received little attention in this field. In this paper, we introduce a method…

Finding diverse solutions in combinatorial problems recently has received considerable attention (Baste et al. 2020; Fomin et al. 2020; Hanaka et al. 2021). In this paper we study the following type of problems: given an integer $k$, the…

Despite the successes of machine learning methods in physical sciences, prediction of the Hamiltonian, and thus electronic properties, is still unsatisfactory. Here, based on graph neural network architecture, we present an extendable…

Time-driven quantum systems are important in many different fields of physics like cold atoms, solid state, optics, etc. Many of their properties are encoded in the time evolution operator which is calculated by using a time-ordered product…

The observed output of an interferometer is the result of interference among the parts of the input light beam traveling along each possible optical path. In complex systems, writing down all these possible optical paths and computing their…

In approximation algorithm design, light spanners has applications in graph-metric problems such as metric TSP (the traveling salesman problem). We have developed an efficient algorithm for light spanners in bounded pathwidth graphs, based…

We introduce a linear-scaling real-space methodology to compute time-resolved electrical responses of materials driven far from equilibrium, with energy relaxation and disorder treated on equal footing. Applying this approach to gapped…

We train a small message-passing graph neural network to predict Hamiltonian cycles on Erd\H{o}s-R\'enyi random graphs in a critical regime. It outperforms existing hand-crafted heuristics after about 2.5 hours of training on a single GPU.…

Photonic chips that integrate guides, switches, gratings and other components, process vast amounts of information rapidly on a single device. A new branch of this technology becomes possible if the light is coupled to cold atoms in a…

Efficiently calculating global illumination has always been one of the greatest challenges in computer graphics. Algorithms for approximating global illumination have always struggled to run in realtime for fully dynamic scenes, and have…

In this paper, we propose an efficient continuation method for locating multiple power flow solutions. We adopt the holomorphic embedding technique to represent solution curves as holomorphic functions in the complex plane. The…

This paper introduces a novel, lightweight method to solve the visibility problem for 2D grids. The proposed method evaluates the existence of lines-of-sight from a source point to all other grid cells in a single pass with no preprocessing…

Recently, one has seen a surge of interest in developing such methods including ones for learning such representations for (undirected) graphs (while preserving important properties). However, most of the work to date on embedding graphs…

In this paper, we give the necessary and sufficient conditions for the existence of Hamiltonian paths in $L-$alphabet and $C-$alphabet grid graphs. We also present a linear-time algorithm for finding Hamiltonian paths in these graphs.