Rivers and Bridges - Lubeck
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This document presents a bridge problem involving drawing a path that crosses each bridge once in a map of the river Trave in Lübeck, Germany. It simplifies the problem by representing it as a graph, where areas of land are vertices and bridges are edges connecting vertices. The graph makes it easier to analyze properties like the number of edges and vertices to determine whether a path crossing all bridges is possible. Modifying the graph, such as by adding more bridges, could change whether such a path exists by altering the graph's properties.
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Graph Theory 117 © David Lippman Creative Commons BY-.docx
Graph Theory 117
© David Lippman Creative Commons BY-SA
Graph Theory and Network Flows
In the modern world, planning efficient routes is essential for business and industry, with
applications as varied as product distribution, laying new fiber optic lines for broadband
internet, and suggesting new friends within social network websites like Facebook.
This field of mathematics started nearly 300 years ago as a look into a mathematical puzzle
(we’ll look at it in a bit). The field has exploded in importance in the last century, both
because of the growing complexity of business in a global economy and because of the
computational power that computers have provided us.
Graphs
Drawing Graphs
Example 1
Here is a portion of a housing development from Missoula, Montana1. As part of her job, the
development’s lawn inspector has to walk down every street in the development making sure
homeowners’ landscaping conforms to the community requirements.
1 Sam Beebe. http://www.flickr.com/photos/sbeebe/2850476641/, CC-BY
118
Naturally, she wants to minimize the amount of walking she has to do. Is it possible for her
to walk down every street in this development without having to do any backtracking?
While you might be able to answer that question just by looking at the picture for a while, it
would be ideal to be able to answer the question for any picture regardless of its complexity.
To do that, we first need to simplify the picture into a form that is easier to work with. We
can do that by drawing a simple line for each street. Where streets intersect, we will place a
dot.
This type of simplified picture is called a graph.
Graphs, Vertices, and Edges
A graph consists of a set of dots, called vertices, and a set of edges connecting pairs of
vertices.
While we drew our original graph to correspond with the picture we had, there is nothing
particularly important about the layout when we analyze a graph. Both of the graphs below
are equivalent to the one drawn above since they show the same edge connections between
the same vertices as the original graph.
You probably already noticed that we are using the term graph differently than you may have
used the term in the past to describe the graph of a mathematical function.
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Graph Theory 119
Example 2
Back in the 18th century in the Prussian city of
Königsberg, a river ran through the city and seven
bridges crossed the forks of the river. The river
and the bridges are highlighted in the picture to
the right2.
As a weekend amusement, townsfolk would see if
they could find a route that would take them
across every bridge once and return them to
where they started.
Leonard Euler (pronoun.
Graph Theory 117 © David Lippman Creative Commons BY-
Graph Theory 117
© David Lippman Creative Commons BY-SA
Graph Theory and Network Flows
In the modern world, planning efficient routes is essential for business and industry, with
applications as varied as product distribution, laying new fiber optic lines for broadband
internet, and suggesting new friends within social network websites like Facebook.
This field of mathematics started nearly 300 years ago as a look into a mathematical puzzle
(we’ll look at it in a bit). The field has exploded in importance in the last century, both
because of the growing complexity of business in a global economy and because of the
computational power that computers have provided us.
Graphs
Drawing Graphs
Example 1
Here is a portion of a housing development from Missoula, Montana1. As part of her job, the
development’s lawn inspector has to walk down every street in the development making sure
homeowners’ landscaping conforms to the community requirements.
1 Sam Beebe. http://www.flickr.com/photos/sbeebe/2850476641/, CC-BY
118
Naturally, she wants to minimize the amount of walking she has to do. Is it possible for her
to walk down every street in this development without having to do any backtracking?
While you might be able to answer that question just by looking at the picture for a while, it
would be ideal to be able to answer the question for any picture regardless of its complexity.
To do that, we first need to simplify the picture into a form that is easier to work with. We
can do that by drawing a simple line for each street. Where streets intersect, we will place a
dot.
This type of simplified picture is called a graph.
Graphs, Vertices, and Edges
A graph consists of a set of dots, called vertices, and a set of edges connecting pairs of
vertices.
While we drew our original graph to correspond with the picture we had, there is nothing
particularly important about the layout when we analyze a graph. Both of the graphs below
are equivalent to the one drawn above since they show the same edge connections between
the same vertices as the original graph.
You probably already noticed that we are using the term graph differently than you may have
used the term in the past to describe the graph of a mathematical function.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O P
Q
R
A
B
C
D
E F
G
H
I
J
K
L
M
N O
P Q
R
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B C
D
E F
G
H
I J
K
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N
O
P
Q
R
Graph Theory 119
Example 2
Back in the 18th century in the Prussian city of
Königsberg, a river ran through the city and seven
bridges crossed the forks of the river. The river
and the bridges are highlighted in the picture to
the right2.
As a weekend amusement, townsfolk would see if
they could find a route that would take them
across every bridge once and return them to
where they started.
Leonard Euler (pronoun ...
Recommended
Graph Theory 117 © David Lippman Creative Commons BY-.docx
Graph Theory 117
© David Lippman Creative Commons BY-SA
Graph Theory and Network Flows
In the modern world, planning efficient routes is essential for business and industry, with
applications as varied as product distribution, laying new fiber optic lines for broadband
internet, and suggesting new friends within social network websites like Facebook.
This field of mathematics started nearly 300 years ago as a look into a mathematical puzzle
(we’ll look at it in a bit). The field has exploded in importance in the last century, both
because of the growing complexity of business in a global economy and because of the
computational power that computers have provided us.
Graphs
Drawing Graphs
Example 1
Here is a portion of a housing development from Missoula, Montana1. As part of her job, the
development’s lawn inspector has to walk down every street in the development making sure
homeowners’ landscaping conforms to the community requirements.
1 Sam Beebe. http://www.flickr.com/photos/sbeebe/2850476641/, CC-BY
118
Naturally, she wants to minimize the amount of walking she has to do. Is it possible for her
to walk down every street in this development without having to do any backtracking?
While you might be able to answer that question just by looking at the picture for a while, it
would be ideal to be able to answer the question for any picture regardless of its complexity.
To do that, we first need to simplify the picture into a form that is easier to work with. We
can do that by drawing a simple line for each street. Where streets intersect, we will place a
dot.
This type of simplified picture is called a graph.
Graphs, Vertices, and Edges
A graph consists of a set of dots, called vertices, and a set of edges connecting pairs of
vertices.
While we drew our original graph to correspond with the picture we had, there is nothing
particularly important about the layout when we analyze a graph. Both of the graphs below
are equivalent to the one drawn above since they show the same edge connections between
the same vertices as the original graph.
You probably already noticed that we are using the term graph differently than you may have
used the term in the past to describe the graph of a mathematical function.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O P
Q
R
A
B
C
D
E F
G
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P Q
R
A
B C
D
E F
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H
I J
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P
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Graph Theory 119
Example 2
Back in the 18th century in the Prussian city of
Königsberg, a river ran through the city and seven
bridges crossed the forks of the river. The river
and the bridges are highlighted in the picture to
the right2.
As a weekend amusement, townsfolk would see if
they could find a route that would take them
across every bridge once and return them to
where they started.
Leonard Euler (pronoun.
Graph Theory 117 © David Lippman Creative Commons BY-
Graph Theory 117
© David Lippman Creative Commons BY-SA
Graph Theory and Network Flows
In the modern world, planning efficient routes is essential for business and industry, with
applications as varied as product distribution, laying new fiber optic lines for broadband
internet, and suggesting new friends within social network websites like Facebook.
This field of mathematics started nearly 300 years ago as a look into a mathematical puzzle
(we’ll look at it in a bit). The field has exploded in importance in the last century, both
because of the growing complexity of business in a global economy and because of the
computational power that computers have provided us.
Graphs
Drawing Graphs
Example 1
Here is a portion of a housing development from Missoula, Montana1. As part of her job, the
development’s lawn inspector has to walk down every street in the development making sure
homeowners’ landscaping conforms to the community requirements.
1 Sam Beebe. http://www.flickr.com/photos/sbeebe/2850476641/, CC-BY
118
Naturally, she wants to minimize the amount of walking she has to do. Is it possible for her
to walk down every street in this development without having to do any backtracking?
While you might be able to answer that question just by looking at the picture for a while, it
would be ideal to be able to answer the question for any picture regardless of its complexity.
To do that, we first need to simplify the picture into a form that is easier to work with. We
can do that by drawing a simple line for each street. Where streets intersect, we will place a
dot.
This type of simplified picture is called a graph.
Graphs, Vertices, and Edges
A graph consists of a set of dots, called vertices, and a set of edges connecting pairs of
vertices.
While we drew our original graph to correspond with the picture we had, there is nothing
particularly important about the layout when we analyze a graph. Both of the graphs below
are equivalent to the one drawn above since they show the same edge connections between
the same vertices as the original graph.
You probably already noticed that we are using the term graph differently than you may have
used the term in the past to describe the graph of a mathematical function.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O P
Q
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P Q
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D
E F
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H
I J
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N
O
P
Q
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Graph Theory 119
Example 2
Back in the 18th century in the Prussian city of
Königsberg, a river ran through the city and seven
bridges crossed the forks of the river. The river
and the bridges are highlighted in the picture to
the right2.
As a weekend amusement, townsfolk would see if
they could find a route that would take them
across every bridge once and return them to
where they started.
Leonard Euler (pronoun ...
Vanmathy no sql
Element of graph four types vertex edge path loop operation of graph three type union of graph intersection of graph graph traversal
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Graph operations
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Graph Analytics - From the Whiteboard to Your Toolbox - Sam Lerma
However, the the graph theory jargon can make graph analytics seem more intimidating for self-study than is necessary. In this talk, the audience will be exposed to some of the basic concepts of graph theory (no prerequisite math knowledge needed!) and a few of the Python tools available for graph analysis.
Graphss
Topological Sort
Given a graph, G = (V, E), output all the vertices in V such that no vertex is output before any other vertex with an edge to it.
An Introduction to Graph Databases
This tutorial will provide you with a basic understanding of graph database technology and the ability to quickly begin development of a graph database application. You will have the capability to recognize graph-based problems and present the benefits of using graph technology for problem resolution.
The tutorial will give you an understanding of:
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• Benefits of graph databases
• Different types of graph databases
• Typical graph database API
• Programming basics
• Use cases
Bring your laptops for a hands-on opportunity to practice some sample codes. A basic understanding of Java programming is a recommended prerequisite to understand this course. This session is led by the InfiniteGraph technical team and the demonstration code will be drawn from InfiniteGraph examples, however the broader educational presentation is product-neutral and not a commercial presentation of their products.
To participate in the hands-on portion of the graph tutorial users must have:
• Java programming experience
• Java Developer Kit (JDK)
• Current InfiniteGraph installed on laptop. (To download visit www.objectivity.com/infinitegraph)
• HelloGraph test – Upon installing IG, run HelloGraph to test the install. (HelloGraph can be found online at http://wiki.infinitegraph.com/2.1/w/index.php?title=Download_Sample_Code)
Leon Guzenda was one of the founding members of Objectivity in 1988 and one of the original architects of Objectivity/DB. He currently works with Objectivity's major customers to help them effectively develop and deploy complex applications and systems that use the industry's highest-performing, most reliable DBMS technology, Objectivity/DB. He also liaises with technology partners and industry groups to help ensure that Objectivity/DB remains at the forefront of database and distributed computing technology. Leon has more than 35 years experience in the software industry. At Automation Technology Products, he managed the development of the ODBMS for the Cimplex solid modeling and numerical control system. Before that, he was Principal Project Director for International Computers Ltd. in the United Kingdom, delivering major projects for NATO and leading multinationals. He was also design and development manager for ICL's 2900 IDMS product. He spent the first 7 years of his career working in defense and government systems. Leon has a B.S. degree in Electronic Engineering from the University of Wales.
Distributed coloring with O(sqrt. log n) bits
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K Kothapalli, M Onus, C Scheideler, C Schindelhauer
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We consider the well-known vertex coloring problem: given a graph G, find a coloring of its vertices so that no two neighbors in G have the same color. It is trivial to see that every graph of maximum degree∆ can be colored with∆+ 1 colors, and distributed algorithms that find a (∆+ 1)-coloring in a logarithmic number of communication rounds, with high probability, are known since more than a decade. This is in general the best possible if only a constant number of bits can be sent along every edge in each round. In fact, we show that for the n-node cycle the bit complexity of the coloring problem is
Ω (log n). More precisely, if only one bit can be sent along each edge in a round, then every distributed coloring algorithm (ie, algorithms in which every node has the same initial state and initially only knows its own edges) needs at least Ω (log n) rounds, with high probability, to color the n–node cycle, for any finite number of colors. But what if the edges have orientations, ie, the endpoints of an edge agree on its orientation (while bits may still flow in both directions)? Edge orientations naturally occur in dynamic networks where new nodes establish connections to old nodes. Does this allow one to provide faster coloring algorithms?
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Vanmathy no sql
Element of graph four types vertex edge path loop operation of graph three type union of graph intersection of graph graph traversal
VANU no sql ppt.pptx
Intruders are the attackers who attempt to breach the security of a network. They attack the network in order to get unauthorized access. Intruders are of three types, namely, masquerader, misfeasor and clandestine user.
Graphs data structures
It includes:
Introduction to Graphs
Applications
Graph representation
Graph terminology
Graph operations
Adding vertex and edge in Adjacency matrix representation using C++ program
Adjacency List implementation in C++
Homework Problems
References
Graph Analytics - From the Whiteboard to Your Toolbox - Sam Lerma
However, the the graph theory jargon can make graph analytics seem more intimidating for self-study than is necessary. In this talk, the audience will be exposed to some of the basic concepts of graph theory (no prerequisite math knowledge needed!) and a few of the Python tools available for graph analysis.
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Topological Sort
Given a graph, G = (V, E), output all the vertices in V such that no vertex is output before any other vertex with an edge to it.
An Introduction to Graph Databases
This tutorial will provide you with a basic understanding of graph database technology and the ability to quickly begin development of a graph database application. You will have the capability to recognize graph-based problems and present the benefits of using graph technology for problem resolution.
The tutorial will give you an understanding of:
• Graph theory - origins and concepts
• Benefits of graph databases
• Different types of graph databases
• Typical graph database API
• Programming basics
• Use cases
Bring your laptops for a hands-on opportunity to practice some sample codes. A basic understanding of Java programming is a recommended prerequisite to understand this course. This session is led by the InfiniteGraph technical team and the demonstration code will be drawn from InfiniteGraph examples, however the broader educational presentation is product-neutral and not a commercial presentation of their products.
To participate in the hands-on portion of the graph tutorial users must have:
• Java programming experience
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• Current InfiniteGraph installed on laptop. (To download visit www.objectivity.com/infinitegraph)
• HelloGraph test – Upon installing IG, run HelloGraph to test the install. (HelloGraph can be found online at http://wiki.infinitegraph.com/2.1/w/index.php?title=Download_Sample_Code)
Leon Guzenda was one of the founding members of Objectivity in 1988 and one of the original architects of Objectivity/DB. He currently works with Objectivity's major customers to help them effectively develop and deploy complex applications and systems that use the industry's highest-performing, most reliable DBMS technology, Objectivity/DB. He also liaises with technology partners and industry groups to help ensure that Objectivity/DB remains at the forefront of database and distributed computing technology. Leon has more than 35 years experience in the software industry. At Automation Technology Products, he managed the development of the ODBMS for the Cimplex solid modeling and numerical control system. Before that, he was Principal Project Director for International Computers Ltd. in the United Kingdom, delivering major projects for NATO and leading multinationals. He was also design and development manager for ICL's 2900 IDMS product. He spent the first 7 years of his career working in defense and government systems. Leon has a B.S. degree in Electronic Engineering from the University of Wales.
Distributed coloring with O(sqrt. log n) bits
Distributed Coloring with O˜(√log n) Bits
K Kothapalli, M Onus, C Scheideler, C Schindelhauer
Proc. of IEEE International Parallel and Distributed Processing Symposium …
We consider the well-known vertex coloring problem: given a graph G, find a coloring of its vertices so that no two neighbors in G have the same color. It is trivial to see that every graph of maximum degree∆ can be colored with∆+ 1 colors, and distributed algorithms that find a (∆+ 1)-coloring in a logarithmic number of communication rounds, with high probability, are known since more than a decade. This is in general the best possible if only a constant number of bits can be sent along every edge in each round. In fact, we show that for the n-node cycle the bit complexity of the coloring problem is
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一比一原版(SFU毕业证)西蒙菲莎大学毕业证成绩单如何办理
SFU毕业证原版定制【微信：176555708】【西蒙菲莎大学毕业证成绩单-学位证】【微信：176555708】（留信学历认证永久存档查询）采用学校原版纸张、特殊工艺完全按照原版一比一制作（包括：隐形水印，阴影底纹，钢印LOGO烫金烫银，LOGO烫金烫银复合重叠，文字图案浮雕，激光镭射，紫外荧光，温感，复印防伪）行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备，十五年致力于帮助留学生解决难题，业务范围有加拿大、英国、澳洲、韩国、美国、新加坡，新西兰等学历材料，包您满意。
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我们所定的价格是非常合理的，而且我们现在做得单子大多数都是代理和回头客户介绍的所以一般现在有新的单子 我给客户的都是第一手的代理价格，因为我想坦诚对待大家 不想跟大家在价格方面浪费时间
对于老客户或者被老客户介绍过来的朋友，我们都会适当给一些优惠。
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Water Industry Process Automation and Control Monthly - May 2024.pdf
Water Industry Process Automation and Control Monthly - May 2024.pdfWater Industry Process Automation & Control
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.WATER CRISIS and its solutions-pptx 1234
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Architectural Portfolio Sean Lockwood
This portfolio contains selected projects I completed during my undergraduate studies. 2018 - 2023
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Final project report on grocery store management system..pdf
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
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Rivers and Bridges - Lubeck
- 1. Lübeck, Germany Rivers and Bridges This bridge problem is a bit more complex than the others, if you haven’t tried any of the other problems try a couple of those first. This is a map of the river Trave in Lübeck, Germany. Can you draw a path that goes over each of the bridges once and only once? Do you think it is possible? Can you prove this? We can simplify this problem into one that we can look at mathematically by drawing the system of rivers and bridges as a graph. By a graph we mean a diagram that shows all the important connections. We mark each area of land as a point (called a vertex) and each bridge as a line (called an edge) joining the two points that represent the land that bridge joins. Have a go at drawing this on top of the map and turn over to see if you got it right.
- 2. Here is a graph of this bridge system: Can you match up each vertex to the area of land it represents? Does the graphs make it easier to answer any of the questions? Think about the properties this graph has e.g. Number of edges Number of vertices Do any of these relate to whether a path across all of the bridges exists? Can you make a change so that it becomes possible/impossible to make a path? For example, do you think adding bridges onto any of the stretches of river that go off the page would change whether a path was possible? Why? What if any of the properties of the graph have you changed?