Dynamic Distribution-Sensitive Point Location

We propose a dynamic data structure for the distribution-sensitive point location problem in the plane. Suppose that there is a fixed query distribution within a convex subdivision S , and we are given an oracle that can return in O (1) time the probability of a query point falling into a polygonal region of constant complexity. We can maintain S such that each query is answered in O opt (S) ) expected time, where opt ( S ) is the expected time of the best linear decision tree for answering point location queries in S . The space and construction time are O(n log 2 n ), where n is the number of vertices of S . An update of S as a mixed sequence of k edge insertions and deletions takes O(k log 4 n) amortized time. As a corollary, the randomized incremental construction of the Voronoi diagram of n sites can be performed in O(n log 4 n ) expected time so that, during the incremental construction, a nearest neighbor query at any time can be answered optimally with respect to the intermediate Voronoi diagram at that time.

Detection and Optimization of Traffic Networks Based on Voronoi Diagram

Traffic peak is an important parameter of modern transport systems. It can be used to calculate the indices of road congestion, which has become a common problem worldwide. With accurate information about traffic peaks, transportation administrators can make better decisions to optimize the traffic networks and therefore enhance the performance of transportation systems. We present a traffic peak detection method, which constructs the Voronoi diagram of the input traffic flow data and computes the prominence of candidate peak points using the diagram. Salient peaks are selected based on the prominence. The algorithm takes O(n log n) time and linear space, where n is the size of the input time series. As compared with the existing algorithms, our approach works directly on noisy data and detects salient peaks without a smoothing prestep and thus avoids the dilemma in choosing an appropriate smoothing scale and prevents the occurrence of removing/degrading real peaks during smoothing step. The prominence of candidate peaks offers the subsequent analysis the flexibility to choose peaks at any scale. Experiments illustrated that the proposed method outperforms the existing smoothing-based methods in sensitivity, positive predictivity, and accuracy.

Methods for calculating the average particulate matter concentrations in the Krasnoyarsk city ground layer

The paper considers a method based on the Voronoi diagram for calculating the average particulate matter concentration in the surface layer of the Krasnoyarsk city air environment. We have used two methods to achieve this goal. The first method relied on buffer zones built in the immediate vicinity around monitoring posts. The second one uses the boundaries of the city of Krasnoyarsk.

Mission Planning for Unmanned Aerial Vehicles Based on Voronoi Diagram-Tabu Genetic Algorithm

Unmanned aerial vehicles (UAVs) are increasingly used in different military missions. In this paper, we focus on the autonomous mission allocation and planning abilities for the UAV systems. Such abilities enable adaptation to more complex and dynamic mission environments. We first examine the mission planning of a single unmanned aerial vehicle. Based on that, we then investigate the multi-UAV cooperative system under the mission background of cooperative target destruction and show that it is a many-to-one rendezvous problem. A heterogeneous UAV cooperative mission planning model is then proposed where the mission background is generated based on the Voronoi diagram. We then adopt the tabu genetic algorithm (TGA) to obtain multi-UAV mission planning. The simulation results show that the single-UAV and multi-UAV mission planning can be effectively realized by the Voronoi diagram-TGA (V-TGA). It is also shown that the proposed algorithm improves the performance by 3% in comparison with the Voronoi diagram-particle swarm optimization (V-PSO) algorithm.

A Path Planning Strategy for Multi-Robot Moving with Path-Priority Order Based on a Generalized Voronoi Diagram

This paper proposes a new path planning strategy called the navigation strategy with path priority (NSPP) for multiple robots moving in a large flat space. In the space, there may be some static or/and dynamic obstacles. Suppose we have the path-priority order for each robot, then this article aims to find an efficient path for each robot from its starting point to its target point without any collision. Here, a generalized Voronoi diagram (GVD) is used to perform the map division based on each robot’s path-priority order, and the proposed NSPP is used to do the path planning for the robots in the space. This NSPP can be applied to any number of robots. At last, there are several simulations with a different number of robots in a circular or rectangular space to be shown that the proposed method can complete the task effectively and has better performance in average trajectory length than those by using the benchmark methods of the shortest distance algorithm (SDA) and reciprocal orientation algorithm (ROA).