A new path planning method based on sparse A* algorithm with map segmentation

Due to the complexity of map modeling, the massive computation and high redundancy of the traditional A* algorithm will greatly reduce the efficiency of pathfinding, resulting in huge performance consumption. Meanwhile, limited by neighborhood search strategy in grid map, the traditional A* algorithm is actually unable to achieve the optimal path in the global sense. To solve these problems, this paper proposes an improved A* algorithm based on graph preprocessing. First, the free space on the map was decomposed into several polygon regions using the improved convex decomposition method based on Maklink. Then, each region was coded into feature nodes according to A* algorithm. Finally, an optimal region passage was found based on the principle of A* algorithm, in which the global optimal path solution was obtained. Compared with the traditional A* algorithm and other classical path planning algorithms, the proposed algorithm has significant advantages in planning speed, path cost, stability, and completeness.

LOCC protocols with bounded width per round optimize convex functions

We start with the task of discriminating finitely many multipartite quantum states using LOCC protocols, with the goal to optimize the probability of correctly identifying the state. We provide two different methods to show that finitely many measurement outcomes in every step are sufficient for approaching the optimal probability of discrimination. In the first method, each measurement of an optimal LOCC protocol, applied to a [Formula: see text]-dimensional local system, is replaced by one with at most [Formula: see text] outcomes, without changing the probability of success. In the second method, we decompose any LOCC protocol into a convex combination of a number of “slim protocols” in which each measurement applied to a [Formula: see text]-dimensional local system has at most [Formula: see text] outcomes. To maximize any convex functions in LOCC (including the probability of state discrimination or fidelity of state transformation), an optimal protocol can be replaced by the best slim protocol in the convex decomposition without using shared randomness. For either method, the bound on the number of outcomes per measurement is independent of the global dimension, the number of parties, the depth of the protocol, how deep the measurement is located, and applies to LOCC protocols with infinite rounds, and the “measurement compression” can be done “top-down” — independent of later operations in the LOCC protocol. The second method can be generalized to implement LOCC instruments with finitely many classical outcomes: if the instrument has [Formula: see text] coarse-grained final measurement outcomes, global input dimension [Formula: see text] and global output dimension [Formula: see text] for [Formula: see text] conditioned on the [Formula: see text]th outcome, then one can obtain the instrument as a convex combination of no more than [Formula: see text] slim protocols; that is, [Formula: see text] bits of shared randomness suffice.

Convergence Rate Analysis of the Proximal Difference of the Convex Algorithm

In this paper, we study the convergence rate of the proximal difference of the convex algorithm for the problem with a strong convex function and two convex functions. By making full use of the special structure of the difference of convex decomposition, we prove that the convergence rate of the proximal difference of the convex algorithm is linear, which is measured by the objective function value.

Maximized Privacy-Preserving Outsourcing on Support Vector Clustering

Despite its remarkable capability in handling arbitrary cluster shapes, support vector clustering (SVC) suffers from pricey storage of kernel matrix and costly computations. Outsourcing data or function on demand is intuitively expected, yet it raises a great violation of privacy. We propose maximized privacy-preserving outsourcing on SVC (MPPSVC), which, to the best of our knowledge, is the first all-phase outsourceable solution. For privacy-preserving, we exploit the properties of homomorphic encryption and secure two-party computation. To break through the operation limitation, we propose a reformative SVC with elementary operations (RSVC-EO, the core of MPPSVC), in which a series of designs make selective outsourcing phase possible. In the training phase, we develop a dual coordinate descent solver, which avoids interactions before getting the encrypted coefficient vector. In the labeling phase, we design a fresh convex decomposition cluster labeling, by which no iteration is required by convex decomposition and no sampling checks exist in connectivity analysis. Afterward, we customize secure protocols to match these operations for essential interactions in the encrypted domain. Considering the privacy-preserving property and efficiency in a semi-honest environment, we proved MPPSVC’s robustness against adversarial attacks. Our experimental results confirm that MPPSVC achieves comparable accuracies to RSVC-EO, which outperforms the state-of-the-art variants of SVC.

A new path planning method based on concave polygon convex decomposition and artificial bee colony algorithm

Free space algorithms are kind of graphics-based methods for path planning. With previously known map information, graphics-based methods have high computational efficiency in providing a feasible path. However, the existing free space algorithms do not guarantee the global optimality because they always search in one connected domain but not all the possible connected domains. To overcome this drawback, this article presents an improved free space algorithm based on map decomposition with multiple connected domains and artificial bee colony algorithm. First, a decomposition algorithm of single-connected concave polygon is introduced based on the principle of concave polygon convex decomposition. Any map without obstacle is taken as single-connected concave polygon (the convex polygon map can be seen as already decomposed and will not be discussed here). Single concave polygon can be decomposed into convex polygons by connecting concave points with their visible vertex. Second, decomposition algorithm for multi-connected concave polygon (any map with obstacles) is designed. It can be converted into single-connected concave polygon by excluding obstacles using virtual links. The map can be decomposed into several convex polygons which form multiple connected domains. Third, artificial bee colony algorithm is used to search the optimal path in all the connected domains so as to avoid falling into the local minimum. Numerical simulations and comparisons with existing free space algorithm and rapidly exploring random tree star algorithm are carried out to evaluate the performance of the proposed method. The results show that this method is able to find the optimal path with high computational efficiency and accuracy. It has advantages especially for complex maps. Furthermore, parameter sensitivity analysis is provided and the suggested values for parameters are given.

Convex Decomposition for a Coverage Path Planning for Autonomous Vehicles: Interior Extension of Edges

To cover an area of interest by an autonomous vehicle, such as an Unmanned Aerial Vehicle (UAV), planning a coverage path which guides the unit to cover the area is an essential process. However, coverage path planning is often problematic, especially when the boundary of the area is complicated and the area contains several obstacles. A common solution for this situation is to decompose the area into disjoint convex sub-polygons and to obtain coverage paths for each sub-polygon using a simple back-and-forth pattern. Aligned with the solution approach, we propose a new convex decomposition method which is simple and applicable to any shape of target area. The proposed method is designed based on the idea that, given an area of interest represented as a polygon, a convex decomposition of the polygon mainly occurs at the points where an interior angle between two edges of the polygon is greater than 180 degrees. The performance of the proposed method is demonstrated by comparison with existing convex decomposition methods using illustrative examples.