相关论文: Solving the Hamiltonian path problem with a light-…

A path graph is the intersection graph of paths in a tree. A directed path graph is the intersection graph of paths in a directed tree. Even if path graphs and directed path graphs are characterized very similarly, their recognition…

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…

We first consider the following problem. We are given a fixed perfect matching $M$ of $[n]$ and we add random edges one at a time until there is a Hamilton cycle containing $M$. We show that w.h.p. the hitting time for this event is the…

We undertake a study on computing Hamiltonian alternating cycles and paths on bicolored point sets. This has been an intensively studied problem, not always with a solution, when the paths and cycles are also required to be plane. In this…

The directed graph reachability problem takes as input an $n$-vertex directed graph $G=(V,E)$, and two distinguished vertices $s$ and $t$. The problem is to determine whether there exists a path from $s$ to $t$ in $G$. This is a canonical…

In the Steiner Path Aggregation Problem, our goal is to aggregate paths in a directed network into a single arborescence without significantly disrupting the paths. In particular, we are given a directed multigraph with colored arcs, a…

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…

femtoPro is an interactive virtual reality (VR) laser laboratory balancing the contrasting challenges of accuracy and computational efficiency in optics simulations. It can simulate linear and nonlinear optical phenomena in real time, a…

Compact representations of objects is a common concept in computer science. Automated planning can be viewed as a case of this concept: a planning instance is a compact implicit representation of a graph and the problem is to find a path (a…

Given $x, y$ on an unweighted undirected graph $G$, the goal of the pathfinding problem is to find an $x$-$y$ path. In this work, we first construct a graph $G$ based on welded trees and define a pathfinding problem in the adjacency list…

Waveguide lattices offer a compact and stable platform for a range of applications, including quantum walks, topological effects, condensed matter system simulation, and classical and quantum information processing. In such lattices, the…

This paper is concerned with the study of a model case of first order Hamilton-Jacobi equations posed on a "junction", that is to say the union of a finite number of half-lines with a unique common point. The main result is a comparison…

Combinatorial optimization algorithms for graph problems are usually designed afresh for each new problem with careful attention by an expert to the problem structure. In this work, we develop a new framework to solve any combinatorial…

Computing paths in graph structures is a fundamental operation in a wide range of applications, from transportation networks to data analysis. The beer path problem, which captures the option of visiting points of interest, such as gas…

In this paper, we propose a graph classification approach for automatically determining whether to use a monolithic or a decomposition-based solution method. In this approach, an optimization problem is represented as a graph that captures…

Consider scene understanding problems such as predicting where a person is probably reaching, or inferring the pose of 3D objects from depth images, or inferring the probable street crossings of pedestrians at a busy intersection. This…

Image matching is a key component of many tasks in computer vision and its main objective is to find correspondences between features extracted from different natural images. When images are represented as graphs, image matching boils down…

A Hamiltonian decomposition of a regular graph is a partition of its edge set into Hamiltonian cycles. The problem of finding edge-disjoint Hamiltonian cycles in a given regular graph has many applications in combinatorial optimization and…

Fundamental theories, such as Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD) promise great predictive power addressing phenomena over vast scales from the microscopic to cosmic scales. However, new non-perturbative tools are…

A hamiltonian sequence is a path walk $P$ that can be a hamiltonian path or hamiltonian circuit. Determining whether such hamiltonian sequence exists in a given graph \G is a NP-Complete problem. In this paper, a novel algorithm for…