Neighbor Search

Neighbor search is a concept in computer science, especially in the fields of data mining and machine learning. It refers to the process of determining the neighboring particles around each particle (usually an atom) in a simulation box. This process is important for calculating interactions between particles, such as van der Waals forces and short-range repulsive forces. It involves quickly locating the point or set of points that are closest to a specific query point in a given dataset.

Since the interactions between particles are usually only significant at short distances, only other particles within a certain range around each particle need to be considered. This range is usually called the cutoff radius. In each time step of the simulation, a neighbor search is required to update the list of particles within this range, because the particles will continue to move during the simulation.

The main purposes of neighbor search include:

1. efficiency：By limiting the calculation scope to neighboring particles, the required amount of calculation can be significantly reduced and the efficiency of the simulation can be improved.
2. accuracy: Ensuring that the interaction forces between particles are correctly calculated within the cutoff radius is crucial to the accuracy of the simulation results.
3. Dealing with non-bonded interactions: Neighbor searching helps deal with pairs of particles that are not connected by chemical bonds but still physically interact.

In actual simulations, neighbor search usually requires building a data structure, such as a grid or linked-cell list, to quickly locate the neighboring particles of each particle. This process is necessary in each simulation step and has a significant impact on performance, so the optimization of neighbor search is an important research direction in high-performance computing. In molecular dynamics software such as GROMACS, neighbor search can be accelerated by CPU or GPU to improve the speed and efficiency of simulation.

The challenge of neighbor search is that as the size of the dataset grows, the computational cost increases significantly, especially in high-dimensional space, which is called the curse of dimensionality. To improve search efficiency, researchers have developed a variety of data structures and algorithms, including kd trees, ball trees, and inverted indexes, which can accelerate the search process in large-scale datasets. In addition, since exact search can be very time-consuming, approximate algorithms are used in many scenarios to quickly find a near-optimal solution.