scholarly journals A survey of the all-pairs shortest paths problem and its variants in graphs

2016 ◽  
Vol 8 (1) ◽  
pp. 16-40 ◽  
Author(s):  
K. R. Udaya Kumar Reddy
Keyword(s):  
Graph Theory ◽  
Spanning Tree ◽  
Average Distance ◽  
Shortest Paths ◽  
Wiener Index ◽  
Exact Results ◽  
Research Directions ◽  
All Pairs Shortest Paths ◽  
Static Version ◽  
Open Issues

Abstract There has been a great deal of interest in the computation of distances and shortest paths problem in graphs which is one of the central, and most studied, problems in (algorithmic) graph theory. In this paper, we survey the exact results of the static version of the all-pairs shortest paths problem and its variants namely, the Wiener index, the average distance, and the minimum average distance spanning tree (MAD tree in short) in graphs (focusing mainly on algorithmic results for such problems). Along the way we also mention some important open issues and further research directions in these areas.

scholarly journals Optimal feeder reconfiguration in distributed generation environment under time-varying loading condition

2021 ◽  
Vol 3 (6) ◽  
Author(s):  
Yanrenthung Odyuo ◽  
Dipu Sarkar ◽  
Lilika Sumi
Keyword(s):  
Graph Theory ◽  
Distributed Generation ◽  
Spanning Tree ◽  
Voltage Stability ◽  
Electrical Network ◽  
List Type ◽  
Network Reconfiguration ◽  
Time Varying ◽  
Electrical Networks ◽  
Tree Algorithm

Abstract The development and planning of optimal network reconfiguration strategies for electrical networks is greatly improved with proper application of graph theory techniques. This paper investigates the application of Kruskal's maximal spanning tree algorithm in finding the optimal radial networks for different loading scenarios from an interconnected meshed electrical network integrated with distributed generation (DG). The work is done with an objective to assess the prowess of Kruskal's algorithm to compute, obtain or derive an optimal radial network (optimal maximal spanning tree) that gives improved voltage stability and highest loss minimization from among all the possible radial networks obtainable from the DG-integrated mesh network for different time-varying loading scenarios. The proposed technique has been demonstrated on a multiple test systems considering time-varying load levels to investigate the performance and effectiveness of the suggested method. For interconnected electrical networks with the presence of distributed generation, it was found that application of Kruskal's algorithm quickly computes optimal radial configurations that gives the least amount of power losses and better voltage stability even under varying load conditions. Article Highlights Investigated network reconfiguration strategies for electrical networks with the presence of Distributed Generation for time-varying loading conditions. Investigated the application of graph theory techniques in electrical networks for developing and planning reconfiguration strategies. Applied Kruskal’s maximal spanning tree algorithm to obtain the optimal radial electrical networks for different loading scenarios from DG-integrated meshed electrical network.

scholarly journals A Survey of User Authentication Based on Channel State Information

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Zhengjie Wang ◽  
Wenwen Dou ◽  
Mingjing Ma ◽  
Xiaoxue Feng ◽  
Zehua Huang ◽  
...  
Keyword(s):  
Channel State Information ◽  
User Authentication ◽  
Human Action ◽  
Fundamental Principle ◽  
Accurate Information ◽  
Channel State ◽  
Research Directions ◽  
State Information ◽  
Device Free ◽  
Open Issues

Recently, human behavior sensing based on WiFi channel state information has drawn more attention in the ubiquitous computing field because it can provide accurate information about the target under a device-free scheme. This paper concentrates on user authentication applications using channel state information. We investigate state-of-the-art studies and survey their characteristics. First, we introduce the concept of channel state information and outline the fundamental principle of user authentication. These systems measure the dynamic channel state information profile and implement user authentication by exploring the channel state information variation caused by users because each user generates unique channel state information fluctuations. Second, we elaborate on signal processing approaches, including signal selection and preprocessing, feature extraction, and classification methods. Third, we thoroughly investigate the latest user authentication applications. Specifically, we analyze these applications from typical human action, including gait, activity, gesture, and stillness. Finally, we provide a comprehensive discussion of user authentication and conclude the paper by presenting some open issues, research directions, and possible solutions.

scholarly journals Average update times for fully-dynamic all-pairs shortest paths

2011 ◽  
Vol 159 (16) ◽  
pp. 1751-1758
Author(s):  
Tobias Friedrich ◽  
Nils Hebbinghaus
Keyword(s):  
Shortest Paths ◽  
All Pairs Shortest Paths

scholarly journals Convex skeletons of complex networks

2018 ◽  
Vol 15 (145) ◽  
pp. 20180422 ◽  
Author(s):  
Lovro Šubelj
Keyword(s):  
Protein Interactions ◽  
Spanning Tree ◽  
Autonomous Systems ◽  
Shortest Paths ◽  
Induced Subgraph ◽  
Social Collaboration ◽  
Computer Scientists ◽  
High Betweenness ◽  
Network Backbone ◽  
Definition Of

A convex network can be defined as a network such that every connected induced subgraph includes all the shortest paths between its nodes. A fully convex network would therefore be a collection of cliques stitched together in a tree. In this paper, we study the largest high-convexity part of empirical networks obtained by removing the least number of edges, which we call a convex skeleton. A convex skeleton is a generalization of a network spanning tree in which each edge can be replaced by a clique of arbitrary size. We present different approaches for extracting convex skeletons and apply them to social collaboration and protein interactions networks, autonomous systems graphs and food webs. We show that the extracted convex skeletons retain the degree distribution, clustering, connectivity, distances, node position and also community structure, while making the shortest paths between the nodes largely unique. Moreover, in the Slovenian computer scientists coauthorship network, a convex skeleton retains the strongest ties between the authors, differently from a spanning tree or high-betweenness backbone and high-salience skeleton. A convex skeleton thus represents a simple definition of a network backbone with applications in coauthorship and other social collaboration networks.

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