相关论文: A Light-Based Device for Solving the Hamiltonian P…
We develop the partitioning technique for quantum discrete systems. The graph consists of several subgraphs: a central graph and several branch graphs, with each branch graph being rooted by an individual node on the central one. We show…
Drawings of non-planar graphs always result in edge crossings. When there are many edges crossing at small angles, it is often difficult to follow these edges, because of the multiple visual paths resulted from the crossings that slow down…
Graph coloring is a problem with varied applications in industry and science such as scheduling, resource allocation, and circuit design. The purpose of this paper is to establish if a new gradient based iterative solver framework known as…
A Hamiltonian cycle of a graph is a closed path that visits each site once and only once. I study a field theoretic representation for the number of Hamiltonian cycles for arbitrary graphs. By integrating out quadratic fluctuations around…
For a connected graph, a path containing all vertices is known as \emph{Hamiltonian path}. For general graphs, there is no known necessary and sufficient condition for the existence of Hamiltonian paths and the complexity of finding a…
We study the Hamilton cycle problem with input a random graph G=G(n,p) in two settings. In the first one, G is given to us in the form of randomly ordered adjacency lists while in the second one we are given the adjacency matrix of G. In…
The derivation of a function is a fundamental tool for solving problems in calculus. Consequently, the motivations for investigating physical systems capable of performing this task are numerous. Furthermore, the potential to develop an…
New solid-state physics based approach is developed for analysis of the paraxial light propagation in two-dimensional (2D) photonic lattices of coupled dielectric waveguides or microcavities. In particular, using Maxwell's equations, a…
The aim of this paper is to present a new method of approximation of planar data set using only arcs or segments. The first problem we are trying to solve is the following: the CNC machines can work only with simple curves (arcs or…
This work develops new numerical methods for the solution of the tomography problem in domains with reflecting obstacles. We compare the solution's performance for Lambertian reflection, for classical tomography with unbroken rays and for…
In this paper, we investigate Hamiltonian path problem in the context of split graphs, and produce a dichotomy result on the complexity of the problem. Our main result is a deep investigation of the structure of $K_{1,4}$-free split graphs…
There are few industries which use manually controlled robots for carrying material and this cannot be used all the time in all the places. So, it is very tranquil to have robots which can follow a specific human by following the unique…
We study solution discovery, where the goal is to obtain a feasible solution to a problem from an initial configuration by a bounded sequence of local moves. In many applications, however, the graph that defines which vertex sets are…
We propose an effective algorithm that enumerates (and actually finds) all 3-edge colorings and Hamiltonian cycles in a cubic graph. The idea is to make a preliminary run that separates the vertices into two types: ``rigid'' (such that the…
Time-resolved illumination provides rich spatio-temporal information for applications such as accurate depth sensing or hidden geometry reconstruction, becoming a useful asset for prototyping and as input for data-driven approaches.…
The signal registered by a plane photodetector placed behind an optically inhomogeneous object irradiated by two coherent Gaussian beams intersecting inside the object at small angle to each other is calculated in the single-scattering…
A recent trend in real-time rendering is the utilization of the new hardware ray tracing capabilities. Often, usage of a distance field representation is proposed as an alternative when hardware ray tracing is deemed too costly, and the two…
The detection of curved lanes is still challenging for autonomous driving systems. Although current cutting-edge approaches have performed well in real applications, most of them are based on strict model assumptions. Similar to other…
The segmentation of transparent objects can be very useful in computer vision applications. However, because they borrow texture from their background and have a similar appearance to their surroundings, transparent objects are not handled…
Conventional nano-photonic schemes minimise multiple scattering to realise a miniaturised version of beam-splitters, interferometers and optical cavities for light propagation and lasing. Here instead, we introduce a nanophotonic network…