Modern Applications of Graph Theory

2021 ◽  
Author(s):  
Vadim Zverovich
Keyword(s):  
Graph Theory ◽  
Molecular Epidemiology ◽  
Emergency Response ◽  
Real Life ◽  
Dominating Sets ◽  
Postgraduate Students ◽  
Graph Theoretic ◽  
Electric Vehicle Charging ◽  
Advanced Students ◽  
Doctoral Dissertations

This book discusses many modern, cutting-edge applications of graph theory, such as traffic networks and Braess’ paradox, navigable networks and optimal routing for emergency response, backbone/dominating sets in wireless sensor networks, placement of electric vehicle charging stations, pedestrian safety and graph-theoretic methods in molecular epidemiology. Because of the rapid growth of research in this field, the focus of the book is on the up-to-date development of the aforementioned applications. The book will be ideal for researchers, engineers, transport planners and emergency response specialists who are interested in the recent development of graph theory applications. Moreover, this book can be used as teaching material for postgraduate students because, in addition to up-to-date descriptions of the applications, it includes exercises and their solutions. Some of the exercises mimic practical, real-life situations. Advanced students in graph theory, computer science or molecular epidemiology may use the problems and research methods presented in this book to develop their final-year projects, master’s theses or doctoral dissertations; however, to use the information effectively, special knowledge of graph theory would be required.

Introduction

2021 ◽  
pp. 1-36
Author(s):  
Vadim Zverovich
Keyword(s):  
Graph Theory ◽  
Biological Networks ◽  
Real Life ◽  
Scale Free ◽  
Graph Theoretic ◽  
Life Problems ◽  
Scale Free Networks ◽  
Web Graph ◽  
The Web

This chapter gives a brief overview of selected applications of graph theory, many of which gave rise to the development of graph theory itself. A range of such applications extends from puzzles and games to serious scientific and real-life problems, thus illustrating the diversity of applications. The first section is devoted to the six earliest applications of graph theory. The next section introduces so-called scale-free networks, which include the web graph, social and biological networks. The last section describes a number of graph-theoretic algorithms, which can be used to tackle a number of interesting applications and problems of graph theory.

Graphs in Molecular Epidemiology

2021 ◽  
pp. 337-388
Author(s):  
Vadim Zverovich
Keyword(s):  
Graph Theory ◽  
Molecular Epidemiology ◽  
Viral Infections ◽  
Virus Evolution ◽  
Transmission Networks ◽  
Immune Systems ◽  
Graph Theoretic ◽  
Graphs And Networks ◽  
Evolution Of Viruses ◽  
Viral Sequences

Graphs and networks are used in molecular epidemiology to model the evolution of viruses and their spread during outbreaks and epidemics. They are instrumental at different stages of the computational pipelines. This includes the inference of transmission networks using viral sequences sampled from infected individuals, and studies of selection and accumulation of mutations in viral populations and their interactions with hosts' immune systems. This chapter describes some algorithmic and graph-theoretic problems associated with these stages to illustrate the relevance of the concepts of graph theory to molecular epidemiology of viral infections. The chapter will demonstrate how graph-theoretic methods combined with the machinery of differential equations, the Bayesian inference, and computational genomics uncover hidden biological and epidemiological patterns of virus evolution and transmission.

scholarly journals SOSerbia: Android-Based Software Platform for Sending Emergency Messages

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Mihailo Jovanovic ◽  
Ivan Babic ◽  
Milan Cabarkapa ◽  
Jelena Misic ◽  
Sasa Mijalkovic ◽  
...  
Keyword(s):  
Emergency Response ◽  
State Of The Art ◽  
Complete Solution ◽  
Real Life ◽  
Android Application ◽  
Unique Combination ◽  
Background Process ◽  
Life Problems ◽  
The Republic ◽  
National Police

This paper presents Android-based SOS platform named SOSerbia for sending emergency messages by citizens in Serbia. The heart of the platform is SOS client Android application which is an easy and simple solution for sending SOS messages with unique combination of volume buttons. The proposed platform solves a lot of safety, security, and emergency problems for people who can be in dangerous situations. After a person presses a correct combination of buttons, a message with his or her location is sent to the operating center of the Serbian Police. The platform merges several appropriately combined advanced Android technologies into one complete solution. The proposed solution also uses the Google location API for getting user’s location and Media Player broadcast receiver for reading pressed buttons for volume. This logic can be also customized for any other mobile operating system. In other words, the proposed architecture can be also implemented in iOS or Windows OS. It should be noted that the proposed architecture is optimized for different mobile devices. It is also implemented with simple widget and background process based on location. The proposed platform is experimentally demonstrated as a part of emergency response center at the Ministry of Interior of the Republic of Serbia. This platform overcomes real-life problems that other state-of-the-art solutions introduce and can be applied and integrated easily in any national police and e-government systems.

scholarly journals Graph Theoretic Techniques in the Analysis of Uniquely Localizable Sensor Networks

2009 ◽  
pp. 146-173 ◽  
Author(s):  
Bill Jackson ◽  
Tibor Jordán
Keyword(s):  
Graph Theory ◽  
Sensor Networks ◽  
Optimization Problems ◽  
Partial Information ◽  
Two Dimensions ◽  
Localization Problem ◽  
Graph Theoretic ◽  
Network Localization ◽  
Exact Location ◽  
The Given

In the network localization problem the goal is to determine the location of all nodes by using only partial information on the pairwise distances (and by computing the exact location of some nodes, called anchors). The network is said to be uniquely localizable if there is a unique set of locations consistent with the given data. Recent results from graph theory and combinatorial rigidity made it possible to characterize uniquely localizable networks in two dimensions. Based on these developments, extensions, related optimization problems, algorithms, and constructions also became tractable. This chapter gives a detailed survey of these new results from the graph theorist’s viewpoint.

scholarly journals COLLEGE STUDENT’S ERROR ANALYSIS BASED ON THEIR MATHEMATICAL CONNECTIONS ON GRAPH REPRESENTATION

2019 ◽  
Vol 4 (1) ◽  
pp. 18
Author(s):  
I ketut Suastika ◽  
Vivi Suwanti
Keyword(s):  
Graph Theory ◽  
College Student ◽  
Real Life ◽  
Graph Representation ◽  
High Ability ◽  
Pilot Studies ◽  
Graph Representations ◽  
Mathematical Connections ◽  
Life Problems ◽  
Basic Concepts

This study is investigates the college student’s errors on their graph representations making based on the mathematical connections indicators. Pilot studies were conducted with 4 college students of middle to high ability in Graph Theory class. Data analyze revealed that top 3 subject’s errors are 1) Finding the relations of a representations to it’s concepts and procedures, 2) Applying mathematics in other sciences or real life problems, and 3) Finding relations among procedures of the equivalent representations. Their lack of graph concepts understanding and it’s connections plays the major role in their errors. They failed at recognizing and choosing the suitable properties of graph which able to detect the error of their graph representation. So, in order to decrease college student errors in graph representations, we need to strengthen their basic concepts and its connections.

scholarly journals Price effect analysis and pre-reseravtion scheme on electric vehicle charging networks

2019 ◽  
Vol 9 (6) ◽  
pp. 5586
Author(s):  
Junghoon Lee ◽  
Gyung-Leen Park
Keyword(s):  
Electric Vehicles ◽  
Service Providers ◽  
Real Life ◽  
Price Effect ◽  
Effect Analysis ◽  
Electric Vehicle Charging ◽  
Demand Patterns ◽  
Charging Stations ◽  
Occupancy Rates ◽  
Charging Demand

<p>This paper investigates the price effect to the charging demand coming from electric vehicles and then evaluates the performance of a pre-reservation mechanism using the real-life demand patterns. On the charging network in Jeju city, the occupancy rates for 3 price groups, namely, free, medium-price, and expensive chargers, are separated almost evenly by about 9.0 %, while a set of chargers dominates the charging demand during hot hours. The virtual pre-reservation scheme matches electric vehicles to a time slot of a charger so as not only to avoid intolerable waiting time in charging stations systematically but also to increase the revenue of service providers, taking into account both bidding levels specified by electric vehicles and preference criteria defined by chargers. The performance analysis results obtained by prototype implementation show that the proposed pre-reservation mechanism improves the revenue of service providers by up to 9.5 % and 42.9 %, compared with the legacy FCFS and reservation-less walk-in schemes for the given performance parameter sets.</p>

Analyzing Distance

2017 ◽  
Author(s):  
Arthur Benjamin ◽  
Gary Chartrand ◽  
Ping Zhang
Keyword(s):  
Graph Theory ◽  
Bipartite Graphs ◽  
Dominating Sets ◽  
Connected Graphs ◽  
Cut Vertex

This chapter considers distance in graphs, first by providing an overview of some fundamental concepts in graph theory. In particular, it discusses connected graphs, cut-vertex and bridge, and bipartite graphs. It then addresses questions of the distance between locations in a graph and those locations that are far from or close to a given location. It also looks at dominating sets in graphs, focusing on the Five Queens Problem/Puzzle and the Lights Out Puzzle, before concluding with an analysis of the rather humorous concept of Erdős numbers, conceptualized by Hungarian mathematician Paul Erdős. According to this concept, for each mathematician A, the Erdős number of A is the distance from A to Erdős in the collaboration graph. Consequently, Erdős is the only mathematician with the Erdős number 0, whereas any mathematician who has coauthored a paper with Erdős has Erdős number 1.

Graph Models for Backbone Sets and Limited Packings in Networks

2021 ◽  
pp. 213-274
Author(s):  
Vadim Zverovich
Keyword(s):  
Fault Tolerant ◽  
Dominating Set ◽  
Facility Location Problem ◽  
Upper Bounds ◽  
Sensor Nodes ◽  
Theoretic Approach ◽  
Dominating Sets ◽  
Packing Number ◽  
Graph Theoretic ◽  
Threshold Functions

Here, a graph-theoretic approach is applied to some problems in networks, for example in wireless sensor networks (WSNs) where some sensor nodes should be selected to behave as a backbone/dominating set to support routing communications in an efficient and fault-tolerant way. Four different types of multiple domination (k-, k-tuple, α‎- and α‎-rate domination) are considered and recent upper bounds for cardinality of these types of dominating sets are discussed. Randomized algorithms are presented for finding multiple dominating sets whose expected size satisfies the upper bounds. Limited packings in networks are studied, in particular the k-limited packing number. One possible application of limited packings is a secure facility location problem when there is a need to place as many resources as possible in a given network subject to some security constraints. The last section is devoted to two general frameworks for multiple domination: <r,s>-domination and parametric domination. Finally, different threshold functions for multiple domination are considered.

THE CUBE-OF-RINGS INTERCONNECTION NETWORK

1998 ◽  
Vol 09 (01) ◽  
pp. 25-37 ◽  
Author(s):  
THOMAS J. CORTINA ◽  
ZHIWEI XU
Keyword(s):  
Graph Theory ◽  
Interconnection Networks ◽  
Fault Tolerant ◽  
Interconnection Network ◽  
Routing Algorithm ◽  
Parallel Computers ◽  
Closed Form Expression ◽  
Form Expression ◽  
Graph Theoretic ◽  
Basic Graph

We present a family of interconnection networks named the Cube-Of-Rings (COR) networks along with their basic graph-theoretic properties. Aspects of group graph theory are used to show the COR networks are symmetric and optimally fault tolerant. We present a closed-form expression of the diameter and optimal one-to-one routing algorithm for any member of the COR family. We also discuss the suitability of the COR networks as the interconnection network of scalable parallel computers.

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