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

Despite their abundance in robotics and nature, underactuated systems remain a challenge for control engineering. Trajectory optimization provides a generally applicable solution, however its efficiency strongly depends on the skill of the…

We propose a new approach to the numerical solution of ergodic problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming…

We show that for each fixed $k$, the problem of finding $k$ pairwise vertex-disjoint directed paths between given source-sink pairs in a planar directed graph is solvable in polynomial time. In fact, it suffices to fix the number of faces…

We present a fast, differentiable, GPU-accelerated optimization method for ray path tracing in environments containing planar reflectors and straight diffraction edges. Based on Fermat's principle, our approach reformulates the path-finding…

The Hamiltonian cycle problem is to decide whether a given graph has a Hamiltonian cycle. Bertossi and Bonuccelli (1986, Information Processing Letters, 23, 195-200) proved that the Hamiltonian Cycle Problem is NP-Complete even for…

Tutte paths are one of the most successful tools for attacking Hamiltonicity problems in planar graphs. Unfortunately, results based on them are non-constructive, as their proofs inherently use an induction on overlapping subgraphs and…

Most of the existing knowledge graphs are not usually complete and can be complemented by some reasoning algorithms. The reasoning method based on path features is widely used in the field of knowledge graph reasoning and completion on…

In this paper, we introduce a graph matching method that can account for constraints of arbitrary order, with arbitrary potential functions. Unlike previous decomposition approaches that rely on the graph structures, we introduce a…

Determining the crossing numbers of Cartesian products of small graphs with arbitrarily large paths has been an ongoing topic of research since the 1970s. Doing so requires the establishment of coincident upper and lower bounds; the former…

We propose an exact algorithm for solving the longest simple path problem between two given vertices in undirected weighted graphs. By using graph partitioning and dynamic programming, we obtain an algorithm that is significantly faster…

The ability to resolve the polarization of light with on-chip devices represents an urgent problem in optoelectronics. The detectors with polarization resolution demonstrated so far mostly require multiple oriented detectors or movable…

A Hamiltonian path (cycle) in a graph is a path (cycle, respectively) which passes through all of its vertices. The problems of deciding the existence of a Hamiltonian cycle (path) in an input graph are well known to be NP-complete, and…

While ray tracing has become increasingly common and path tracing is well understood by now, a major challenge lies in crafting an easy-to-use and efficient system implementing these technologies. Following a purely physically-based…

In this paper, we introduce a so-called Multistage graph Simple Path (MSP) problem and show that the Hamilton Circuit (HC) problem can be polynomially reducible to the MSP problem. To solve the MSP problem, we propose a polynomial algorithm…

We consider light propagation through a twisted nematic liquid crystal. At first, an expression for light transmission is obtained using a rather intuitive approach. Secondly, an accurate solution for light transmission based on Maxwell's…

Our studies are related to a special class of FASS-curves, which can be described in a node-rewriting Lindenmayer-system. These ortho-tile (or diagonal) type recursive curves inducing Hamiltonian paths. We define a special directed graph on…

Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental…

We present an approach for the study and design of reflectors with rotational or translational symmetry that redirect light from a point source into any desired radiant intensity distribution. This method is based on a simple conformal map…

Investigation of light in the waveguide structures is a topical modern problem that has long historical roots. A parallel-plate waveguide is a base model in these studies and it is intensively used in numerous investigations of nanooptics,…

Recent differentiable rendering techniques have become key tools to tackle many inverse problems in graphics and vision. Existing models, however, assume steady-state light transport, i.e., infinite speed of light. While this is a safe…