The spatial optimization method between combinatorial optimization problems and GIS has many geographical applications. The p-center problem is a classic NP-hard location modeling problem, which has essential applications in many real-world scenarios, such as urban facility locations (ambulances, fire stations, pipelines maintenance centers, police stations, etc.). This study implements two methods to solve this problem: an exact algorithm and an approximate algorithm. Exact algorithms can get the optimal solution to the problem, but they are inefficient and time-consuming. The approximate algorithm can give the sub-optimal solution of the problem in polynomial time, which has high efficiency, but the accuracy of the solution is closely related to the initialization center point. We propose a new paradigm that combines a graph convolution network and greedy algorithm to solve the p-center problem through direct training and realize that the efficiency is faster than the exact algorithm. The accuracy is superior to the heuristic algorithm. We generate a large amount of p-center problems by the Erdos–Renyi graph, which can generate instances in many real problems. Experiments show that our method can compromise between time and accuracy and affect the solution of p-center problems.

In this work, we investigate the existence and uniqueness of the solutions for a class of nonlinear fractional differential equations with nonlocal integral boundary conditions. Our analysis relies on the fixed point index theory and a $u_{0}$ -positive operator. Examples are discussed for the illustration of the main work.

Ontology plays an important role in locating Domain-Specific Deep Web contents, therefore, this paper presents a novel framework WFF for efficiently locating Domain-Specific Deep Web databases based on focused crawling and ontology by constructing Web Page Classifier(WPC), Form Structure Classifier(FSC) and Form Content Classifier(FCC) in a hierarchical fashion. Firstly, WPC discovers potentially interesting pages based on ontology-assisted focused crawler. Then, FSC analyzes the interesting pages and determines whether these pages subsume searchable forms based on structural characteristics. Lastly, FCC identifies searchable forms that belong to a given domain in the semantic level, and stores these URLs of Domain- Specific searchable forms to a database. Through a detailed experimental evaluation, WFF framework not only simplifies discovering process, but also effectively determines Domain-Specific databases.

The ability to quickly calculate or query the shortest path distance between nodes on a road network is essential for many real-world applications. However, the traditional graph traversal shortest path algorithm methods, such as Dijkstra and Floyd–Warshall, cannot be extended to large-scale road networks, or the traversal speed on large-scale networks is very slow, which is computational and memory intensive. Therefore, researchers have developed many approximate methods, such as the landmark method and the embedding method, to speed up the processing time of graphs and the shortest path query. This study proposes a new method based on landmarks and embedding technology, and it proposes a multilayer neural network model to solve this problem. On the one hand, we generate distance-preserving embedding for each node, and on the other hand, we predict the shortest path distance between two nodes of a given embedment. Our approach significantly reduces training time costs and is able to approximate the real distance with a relatively low Mean Absolute Error (MAE). The experimental results on a real road network confirm these advantages.