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The distribution of emergency perishable materials is crucial for rescue operations in disaster-stricken areas. However, the freshness of these materials changes over time, affecting the quantity of materials that can be distributed to demand points at different stages. To address this issue, this paper proposes a novel approach. Firstly, a piecewise function is constructed to describe the impact of freshness on the quality and quantity of emergency perishable materials at different time stages. Secondly, the paper establishes a vehicle distribution optimization model with the goal of maximizing the sum of the freshness of all emergency perishable materials delivered to different disaster-affected locations, taking into account the different minimum freshness constraints for the same kind of materials in different locations. Thirdly, an approximate algorithm is designed to solve the model, with the time complexity and the upper and lower bounds of the approximate ratio analyzed. Finally, an example analysis is conducted to demonstrate the validity of the proposed model and algorithm. [ABSTRACT FROM AUTHOR]

As social networks grow, they become more and more complex, and analyzing them becomes complicated. One way to reduce this complexity is to divide the network into subnets, which are also called communities. Dividing social networks into desirable communities can help analysts and experts to understand the behavior and function of the networks. Community detection in networks is a challenging topic in network science and various methods have been proposed for that. Modularity maximization is one of the state-of-the-art methods suggested for community detection. Modularity maximization is an NP-hard problem meaning that no polynomial-time algorithm exists that could solve the problem optimally unless P=NP. A group of approaches that could solve such problems is approximate algorithms. Identifying the influential nodes has many important applications in social networks. This technique could also be used in community detection. To maximize modularity, in this paper, we propose approximate algorithms based on identifying the influential nodes and their influence domain. We used the concept of scale-free networks to prove the approximate factor. Experiments on real-world networks show that the proposed algorithm can compete with the state-of-the-art methods of community detection algorithms. [ABSTRACT FROM AUTHOR]

As social networks grow, they become more and more complex, and analyzing them becomes complicated. One way to reduce this complexity is to divide the network into subnets, which are also called communities. Dividing social networks into desirable communities can help analysts and experts to understand the behavior and function of the networks. Community detection in networks is a challenging topic in network science and various methods have been proposed for that. Modularity maximization is one of the state-of-the-art methods suggested for community detection. Modularity maximization is an NP-hard problem meaning that no polynomial-time algorithm exists that could solve the problem optimally unless P=NP. A group of approaches that could solve such problems is approximate algorithms. Identifying the influential nodes has many important applications in social networks. This technique could also be used in community detection. To maximize modularity, in this paper, we propose approximate algorithms based on identifying the influential nodes and their influence domain. We used the concept of scale-free networks to prove the approximate factor. Experiments on real-world networks show that the proposed algorithm can compete with the state-of-the-art methods of community detection algorithms. [ABSTRACT FROM AUTHOR]

Graphs (networks) are an important tool to model data in different domains. Realworld graphs are usually directed, where the edges have a direction and they are not symmetric. Betweenness centrality is an important index widely used to analyze networks. In this paper, first given a directed network G and a vertex r ∈ V (G), we propose an exact algorithm to compute betweenness score of r. Our algorithm pre-computes a set ℛ(r), which is used to prune a huge amount of computations that do not contribute to the betweenness score of r. Time complexity of our algorithm depends on |ℛ(r)| and it is respectively Θ(|ℛ(r)| · |E(G)|) and Θ(|ℛ(r)| · |E(G)| + |ℛ(r)| · |V(G)| log |V(G)|) for unweighted graphs and weighted graphs with positive weights. |ℛ(r)| is bounded from above by |V(G)| – 1 and in most cases, it is a small constant. Then, for the cases where ℛ(r) is large, we present a simple randomized algorithm that samples from ℛ(r) and performs computations for only the sampled elements. We show that this algorithm provides an (ɛ, δ)-approximation to the betweenness score of r. Finally, we perform extensive experiments over several real-world datasets from different domains for several randomly chosen vertices as well as for the vertices with the highest betweenness scores. Our experiments reveal that for estimating betweenness score of a single vertex, our algorithm significantly outperforms the most efficient existing randomized algorithms, in terms of both running time and accuracy. Our experiments also reveal that our algorithm improves the existing algorithms when someone is interested in computing betweenness values of the vertices in a set whose cardinality is very small. [ABSTRACT FROM AUTHOR]

As a major type of continuous spatial queries, the moving k nearest neighbor (kNN) query has been studied extensively. However, most existing studies have focused on only the query efficiency. In this paper, we consider further the usability of the query results, in particular the diversification of the returned data points. We thereby formulate a new type of query named the moving k diversified nearest neighbor query (MkDNN). This type of query continuously reports the k diversified nearest neighbors while the query object is moving. Here, the degree of diversity of the kNN set is defined on the distance between the objects in the kNN set. Computing the k diversified nearest neighbors is an NP-hard problem. We propose an algorithm to maintain incrementally the k diversified nearest neighbors to reduce the query processing costs. We further propose two approximate algorithms to obtain even higher query efficiency with precision bounds. We verify the effectiveness and efficiency of the proposed algorithms both theoretically and empirically. The results confirm the superiority of the proposed algorithms over the baseline algorithm. [ABSTRACT FROM PUBLISHER]