Related papers: Finding pathways between distant local minima
An analysis of the network defined by the potential energy minima of multi-atomic systems and their connectivity via reaction pathways that go through transition states allows to understand important characteristics like thermodynamic,…
Traveling to different destinations is a big part of our lives. We visit a variety of locations both during our daily lives and when we're on vacation. How can we find the best way to navigate from one place to another? Perhaps we can test…
Shortest path algorithms have played a key role in the past century, paving the way for modern day GPS systems to find optimal routes along static systems in fractions of a second. One application of these algorithms includes optimizing the…
A modified version of the Dijkstra algorithm using an inventive contraction hierarchy is proposed. The algorithm considers a directed acyclic graph with a conical or semi-circular structure for which a pair of edges is chosen iteratively…
Popular methods for identifying transition paths between energy minima, such as the nudged elastic band and string methods, typically do not incorporate potential energy curvature information, leading to slow relaxation to the minimum…
Path finding algorithm addresses problem of finding shortest path from source to destination avoiding obstacles. There exist various search algorithms namely A*, Dijkstra's and ant colony optimization. Unlike most path finding algorithms…
Stable states in complex systems correspond to local minima on the associated potential energy surface. Transitions between these local minima govern the dynamics of such systems. Precisely determining the transition pathways in complex and…
Understanding how complex systems transition between states requires mapping the energy landscape that governs these changes. Local transition-state networks reveal the barrier architecture that explains observed behaviour and enables…
Dijkstra's algorithm is the standard method for computing shortest paths on arbitrary graphs. However, it is slow for large graphs, taking at least linear time. It has been long known that for real world road networks, creating a hierarchy…
The probability of trajectories of weakly diffusive processes to remain in the tubular neighbourhood of a smooth path is given by the Freidlin-Wentzell-Graham theory of large deviations. The most probable path between two states (the…
Given a multidimensional free-energy or potential-energy landscape, finding reaction paths that connect an initial (or reactant) state and a final (or product) state is important for biophysics and materials science. The likelihood of a…
Shortest path computation is a fundamental problem in road networks. However, in many real-world scenarios, determining solely the shortest path is not enough. In this paper, we study the problem of finding k-Dissimilar Paths with Minimum…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
We present a new efficient transition pathway search method based on the least action principle and the Gaussian process regression method. Most pathway search methods developed so far rely on string representations, which approximate a…
In this paper we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is…
In this paper, we propose a new method for path planning to a point for robot in environment with obstacles. The resulting algorithm is implemented as a simple variation of Dijkstra's algorithm. By adding a constraint to the shortest-path,…
GPS receivers embedded in cell phones and connected vehicles generate a series of location measurements that can be used for various analytical purposes. A common pre-processing step of this data is the so-called map matching. The goal of…
A method combining denoising diffusion probabilistic models (DDPMs) with the string method is presented to generate minimum free energy paths between metastable states in molecular systems. It has been demonstrated in recent work that DDPMs…
We develop new algorithmic techniques for VLSI detailed routing. First, we improve the goal-oriented version of Dijkstra's algorithm to find shortest paths in huge incomplete grid graphs with edge costs depending on the direction and the…
We study the connected ensemble, a statistical-mechanics framework that characterizes the formation of low-loss paths in rugged landscapes. First introduced in a previous paper, this ensemble allows one to identify when a network can be…