SlideShare una empresa de Scribd logo
1 de 82
Introduction to Graphs
• A graph G is simply a set V of vertices/nodes
and a collection E of pairs of vertices from V,
called edges/arcs.
11
55
44
33
22
Vertices v={1,2,3,4,5}
Edges={ (1,4), (1,2), (2,3), (3,5),(4,3) }
• Some times edges have third component called
weight or cost. Such graphs are called weighted
graphs
• Edges in a graph are either directed or undirected.
• An edge {u,v} is said to be undirected if
edge (u,v) = edge (v,u)
• An edge (u,v) is said to be directed if (u,v) and
(v,u) edges are not same and represented by two
different lines.
• If all the edges in a graph are undirected, then
we say the graph is an undirected graph.
• a directed graph, also called a digraph, is a
graph whose edges are all directed.
• A graph that has both directed and undirected
edges is often called a mixed graph.
11
55 44
33
22
11
55
44
33
22
verticesvertices
Undirected
Edge
Undirected
Edge
Directed
Edge
(1,4)
Directed
Edge
(1,4)
• Vetex u is adjacent to vertex v if there exists an
edge between u and v in the graph
• An edge is said to be incident on a vertex if the
vertex is one of the edge’s endpoints.
11
55 44
33
22
11
55
44
33
22
vertices 1
and 2 are
adjacent
vertices 1
and 2 are
adjacent
Outgoing
Edges 2
Outgoing
Edges 2
Incoming
Edges 2
Incoming
Edges 2
• The degree of a vertex v, denoted deg(v), is
the number of incident edges of v. The in-
degree and out-degree of a vertex v are the
number of the incoming and outgoing edges
of v, and are denoted indeg(v) and outdeg(v),
respectively.
11
55
44
33
22
Degree of 3 is 3Degree of 3 is 3
In Degree of 3 is 2In Degree of 3 is 2
Out Degree of 3 is 1Out Degree of 3 is 1
Degree of 4 is 2Degree of 4 is 2
In Degree of 4 is 1In Degree of 4 is 1
Out Degree of 4 is 1Out Degree of 4 is 1
An edge (undirected or directed) is a self-loop
if its two endpoints coincide
An edge (undirected or directed) is a self-loop
if its two endpoints coincide
A graphs do not have parallel edges or self-
loops such graphs are said to be simple graph.
A graphs do not have parallel edges or self-
loops such graphs are said to be simple graph.
AA
CC
BB
DD
e1e1
e2e2
e3e3
e5e5
e4e4
AA
CC
BB
DD
self-loopself-loop
simplesimple
• Connected Graph: any two vertices are
connected by some path. All vertices can be
reached by all other vertices in graph
• Tree is a connected graph without cycles
• Simple path : no repeated vertex
Cycle: simple path, except that the last vertex is
same as the first
• Directed graphs that have no cycles are called
Directed acyclic graphs (DAG)
• A undirected graph is connected if there is a
edge from every vertex to every other vertex.
• Directed connected graphs are called strongly
connected
Real life situations that can be modelled by a graph
1) Airport System
Vetex : airports
Edges: flight routes
Edge cost: time, distance or cost
Graph is directed graph as cost may not be the same for
to and fro journey
Make sure the graph is strongly connected so that every
airport is connected
We must also determine the best path (having less cost)
between any 2 airports
Two vertices are connected by an edge is there exists a
non stop flight from the airports
Traffic Flow
• Vertex: each street intersection
• Edge : each street
• Edge cost: speed limit or capacity
• We can find shortest route or most likely
location for bottlenecks
1. Adjacency Matrix1. Adjacency Matrix
2. Adjacency List2. Adjacency List
Graph RepresentationGraph Representation
Adjacency Matrix
• Assume V = {1, 2, …, n}
• An adjacency matrix represents the graph as a
n x n matrix A:
– A[i, j] = 1 if edge (i, j) ∈ E (or weight of edge)
= 0 if edge (i, j) ∉ E
– Storage requirements: O(V2
)
• A dense representation
AA
CC
BB
DD
1. Adjacency Matrix1. Adjacency Matrix
AA BB CC DD
AA
BB
CC
DD
00 11 00 11
11 00 11 11
00 11 00 11
11 11 11 11
AA
CC
BB
DD
1. Adjacency Matrix1. Adjacency Matrix
AA BB CC DD
AA
BB
CC
DD
00 11 00 11
00 00 11 11
00 00 00 00
00 00 11 11
For a digraph (= directed graph), the row sum is the
out_degree, while the column sum is the in_degree
AA
DD
BB
CC
2. Adjacency List2. Adjacency List
AAAA
BBBB
CCCC
DDDD
BBBB DDDD
DDDD
AAAA BBBB DDDD
AAAA
Adjacency ListAdjacency List
An undirected graph with n vertices and e edges
has n head nodes and 2e list nodes in
adjacency list
Nodes that have direct edges are only added as
list nodes to that node.
In the above example, node A has direct edges
with node B and node D
Graph Traversals
Graph traversal is a technique used for searching vertex in a
graph. The graph traversal is also used to decide the order of
vertices to be visited in the search process. A graph traversal
finds the edges to be used in the search process without
creating loops. That means using graph traversal we visit all the
vertices of graph without visiting the vertices that are already
visited.
Two types of graph traversals
1.Breadth first search (BFS)
2.Depth first search (DFS)
BFS and DFS produces a spanning tree as final result.
BFS are implemented using Queues and DFS using Stacks
Step 1: Start
Step 2: Read the graph
Step 3:Define a Queue of size = total number of vertices in the graph.
Step 4: Mark all the vertices as unvisited.
Step 5:Select any node as starting vertex (say v1). Insert v1 into queue.
Step 6: Visit all the non-visited adjacent vertices of the vertex which is at front of
the Queue and insert them into the Queue and mark them visited.
Step 7- When there is no new vertex to be visited from the vertex which is at front
of the Queue then delete that vertex.
Step 8 - Repeat steps 6 and 7 until queue becomes empty.
Step 9- When queue becomes empty, then produce final spanning tree by
removing unused edges from the graph
Step 10: stop
Breadth-First Search Algorithm
#include<stdio.h>
int a[20][20],q[20],visited[20],n,f=-1,r=-1;
void bfs(int v)
{
int i;
for (i=0;i<n;i++) // check all the vertices in the graph
{
if(a[v][i] != 0 && visited[i] == 0) // adjacent to v and not visited
{
r=r+1;
q[r]=i; // insert them into queue
visited[i]=1; // mark the vertex visited
printf("%d ",i);
}
}
f=f+1; // remove the vertex at front of the queue
if(f<=r) // as long as there are elements in the queue
bfs(q[f]); // peform bfs again on the vertex at front of the queue
}
Entire program is at below link
http://enthusiaststudent.blogspot.com/2019/03/breadth-first-search-c-program.html
BFS Program
BFS traversal is A ->
BFS traversal is A -> D -> E -> B
BFS traversal is A -> D -> E -> B
BFS traversal is A -> D -> E -> B -> C -> F
BFS traversal is A -> D -> E -> B -> C -> F
BFS traversal is A -> D -> E -> B -> C -> F -> G
BFS traversal is A -> D -> E -> B -> C -> F -> G
BFS traversal is A -> D -> E -> B -> C -> F -> G
BFS traversal is A -> D -> E -> B -> C -> F -> G
Depth-First Search Algorithm
Step 1 - Define a Stack of size = total number of vertices in the graph.
Step 2 - Select any vertex as starting point for traversal. Visit that vertex and
push it on to the Stack.
Step 3 - Visit any one of the non-visited adjacent vertices of a vertex which is
at the top of stack and push it on to the stack.
Step 4 - Repeat step 3 until there is no new vertex to be visited from the vertex
which is at the top of the stack.
Step 5 - When there is no new vertex to visit then use back tracking and pop
one vertex from the stack.
Step 6 - Repeat steps 3, 4 and 5 until stack becomes Empty.
Step 7 - When stack becomes Empty, then produce final spanning tree by
removing unused edges from the graph
#include<stdio.h>
int a[20][20],q[20],visited[20],n;
void dfs(int v)
{
int i;
for (i=0;i<n;i++) // check all the vertices in the graph
{
if(a[v][i] != 0 && visited[i] == 0) // adjacent to v and not visited
{
visited[i]=1; // mark the vertex visited
printf("%d ",i);
dfs(i);
}
}
}
Entire program is at below link
http://enthusiaststudent.blogspot.com/2019/03/depth-first-search-c-program.html
DFS Program
DFS traversal is A
DFS traversal is A -> B
DFS traversal is A -> B -> C
DFS traversal is A -> B -> C -> E
DFS traversal is A -> B -> C -> E -> D
DFS traversal is A -> B -> C -> E -> D
DFS traversal is A -> B -> C -> E -> D -> F
DFS traversal is A -> B -> C -> E -> D -> F -> G
DFS traversal is A -> B -> C -> E -> D -> F -> G
DFS traversal is A -> B -> C -> E -> D -> F -> G
DFS traversal is A -> B -> C -> E -> D -> F -> G
DFS traversal is A -> B -> C -> E -> D -> F -> G
DFS traversal is A -> B -> C -> E -> D -> F -> G
DFS traversal is A -> B -> C -> E -> D -> F -> G
DFS traversal is A -> B -> C -> E -> D -> F -> G
Topological sorting for Directed Acyclic Graph (DAG) is a
linear ordering of vertices such that for every directed edge (u,v),
vertex u comes before v in the ordering. Topological Sorting for a
graph is not possible if the graph is not a DAG.
For example : consider a graph represents the course
prerequisite structure at a university.
A directed edge (v,w) indicates that course v must be completed
before course w may be attempted. A topological ordering of these
courses is any course sequence that does not violate the prerequisite
requirement.
It is clear that a topological ordering is not possible if the graph
has a cycle, since for two vertices v and w on the cycle, v precedes w
and w precedes v. Furthermore, the ordering is not necessarily
unique; any legal ordering will do.
Topological Sort
Step 1: Identify vertices that have no incoming edges
•
•
If no such vertices, graph has only cycle(s) (cyclic graph)
Topological sort not possible – Halt.
B
C
A
Example of a cyclic graph
D
Topological Sort
Step 1: Identify vertices that have no incoming edges
• The “in-degree” of these vertices is zero
B
C
A
F
D E
Topological Sort
Step 2: Delete this vertex of in-degree 0 and all
its outgoing edges
output.
B
A
from the graph. Place it in the
C
AF
D E
Topological Sort
Repeat Step 1 and Step 2 until graph is empty
Select
B
C
AF
D E
Topological Sort
B
Select B. Copy to sorted list. Delete B and its edges.
B
C
A BF
D E
C
Select C. Copy to sorted list. Delete C and its edges.
C
A B CF
D E
D
Select D. Copy to sorted list. Delete D and its edges.
DA B CF
D E
E, F
Select
Select
E.
F.
Copy
Copy
to
to
sorted
sorted
list.
list.
Delete
Delete
E and its edges.
F and its edges.
DA B C E FF
E
Done
B
C
A
F
Remove from algorithm
and serve.D E
DA B C E F
Topological Ordering Algorithm:
Example
58
v1
Topological order:
v2 v3
v6 v5 v4
v7 v1
Topological Ordering Algorithm:
Example
59
v2
Topological order: v1
v2 v3
v6 v5 v4
v7
Topological Ordering Algorithm:
Example
60
v3
Topological order: v1, v2
v3
v6 v5 v4
v7
Topological Ordering Algorithm:
Example
61
v4
Topological order: v1, v2, v3
v6 v5 v4
v7
Topological Ordering Algorithm:
Example
62
v5
Topological order: v1, v2, v3, v4
v6 v5
v7
Topological Ordering Algorithm:
Example
63
v6
Topological order: v1, v2, v3, v4, v5
v6
v7
Topological Ordering Algorithm:
Example
64
v7
Topological order: v1, v2, v3, v4, v5, v6
v7
Minimum spanning trees
A spanning tree for  a connected graph G (V,E)   with n vertices is a tree 
containing all the vertices of G and n-1 edges. The spanning tree must be 
connected and must not have cycles.
The cost of the spanning tree is the sum of the weights of all the edges in the tree. 
There can be many spanning trees. Minimum spanning tree is the spanning tree 
where the cost is minimum among all the spanning trees. There also can be many 
minimum spanning trees.
Minimum Spanning Tree Algorithms
Kruskal’s algorithm
1. Select the shortest edge in the 
graph
2. Select the next shortest edge 
which does not create a cycle
3. Repeat step 2 until all vertices 
have been connected
Prim’s algorithm
1. Select any vertex
2. Select the shortest edge 
connected to that vertex which 
does not create a cycle
3. Select the shortest edge 
connected to any vertex already 
connected which does not 
create a cycle
4. Repeat step 3 until all vertices 
have been connected
A cable company want to connect five villages to their network which
currently extends to the market town of Tirupati. What is the minimum
length of cable needed?
Tirupathi kadapa
Vijayawada
Bangalore
kurnool
Chennai
2
7
4
5
8 6
4
5
3
8
Example
We model the situation as a network, then the
problem is to find the minimum spanning tree for the
network
A F
B C
D
E
2
7
4
5
8 6
4
5
3
8
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
List the edges in 
order of size:
ED  2
AB  3
AE  4
CD  4
BC  5
EF  5
CF  6
AF  7
BF  8
CF  8
Kruskal’s Algorithm
Select the shortest
edge in the network
ED 2
Kruskal’s Algorithm
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Select the next shortest
edge which does not
create a cycle
ED 2
AB 3
Kruskal’s Algorithm
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Select the next shortest
edge which does not
create a cycle
ED 2
AB 3
CD 4 (or AE 4)
Kruskal’s Algorithm
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Select the next shortest
edge which does not
create a cycle
ED 2
AB 3
CD 4
AE 4
Kruskal’s Algorithm
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Select the next shortest
edge which does not
create a cycle
ED 2
AB 3
CD 4
AE 4
BC 5 – forms a cycle
EF 5
Kruskal’s Algorithm
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
All vertices have been
connected.
The solution is
ED 2
AB 3
CD 4
AE 4
EF 5
Total weight of tree: 18
Kruskal’s Algorithm
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Select any vertex
A
Select the shortest 
edge connected to 
that vertex
AB  3
Prim’s Algorithm
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Select the shortest
edge connected to 
any vertex already 
connected.
AE  4
Prim’s Algorithm
Select the shortest
edge connected to 
any vertex already 
connected.
ED  2
Prim’s Algorithm
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Select the shortest
edge connected to 
any vertex already 
connected.
DC  4
Prim’s Algorithm
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Select the shortest
edge connected to 
any vertex already 
connected.
EF  5  
Prim’s Algorithm
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
Prim’s Algorithm
A
F
B
C
D
E
2
7
4
5
8 6
4
5
3
8
All vertices have been
connected.
The solution is
AB 3
AE 4
ED 2
DC 4
EF 5
Total weight of tree: 18
•Both algorithms will always give solutions with the
same length.
•They will usually select edges in a different order
– you must show this in your workings.
•Occasionally they will use different edges – this
may happen when you have to choose between
edges with the same length. In this case there is
more than one minimum connector for the
network.
Some points to note

Más contenido relacionado

La actualidad más candente

Python Data Structures and Algorithms.pptx
Python Data Structures and Algorithms.pptxPython Data Structures and Algorithms.pptx
Python Data Structures and Algorithms.pptxShreyasLawand
 
Uvm dcon2013
Uvm dcon2013Uvm dcon2013
Uvm dcon2013sean chen
 
Dijkstra s algorithm
Dijkstra s algorithmDijkstra s algorithm
Dijkstra s algorithmmansab MIRZA
 
Data structure - Graph
Data structure - GraphData structure - Graph
Data structure - GraphMadhu Bala
 
Data Structure and Algorithms Hashing
Data Structure and Algorithms HashingData Structure and Algorithms Hashing
Data Structure and Algorithms HashingManishPrajapati78
 
Bellman ford algorithm
Bellman ford algorithmBellman ford algorithm
Bellman ford algorithmA. S. M. Shafi
 
Threaded binarytree&heapsort
Threaded binarytree&heapsortThreaded binarytree&heapsort
Threaded binarytree&heapsortSsankett Negi
 
Applications of graphs
Applications of graphsApplications of graphs
Applications of graphsTech_MX
 
Chap 7 binary threaded tree
Chap 7 binary threaded treeChap 7 binary threaded tree
Chap 7 binary threaded treeRaj Sarode
 
Presentation on binary search, quick sort, merge sort and problems
Presentation on binary search, quick sort, merge sort  and problemsPresentation on binary search, quick sort, merge sort  and problems
Presentation on binary search, quick sort, merge sort and problemsSumita Das
 
Prims and kruskal algorithms
Prims and kruskal algorithmsPrims and kruskal algorithms
Prims and kruskal algorithmsSaga Valsalan
 
Dijkstra algorithm a dynammic programming approach
Dijkstra algorithm   a dynammic programming approachDijkstra algorithm   a dynammic programming approach
Dijkstra algorithm a dynammic programming approachAkash Sethiya
 
Hash table
Hash tableHash table
Hash tableVu Tran
 

La actualidad más candente (20)

Python Data Structures and Algorithms.pptx
Python Data Structures and Algorithms.pptxPython Data Structures and Algorithms.pptx
Python Data Structures and Algorithms.pptx
 
AVL tree animation.ppt
AVL tree animation.pptAVL tree animation.ppt
AVL tree animation.ppt
 
Uvm dcon2013
Uvm dcon2013Uvm dcon2013
Uvm dcon2013
 
Dijkstra s algorithm
Dijkstra s algorithmDijkstra s algorithm
Dijkstra s algorithm
 
Data structure - Graph
Data structure - GraphData structure - Graph
Data structure - Graph
 
Data Structure and Algorithms Hashing
Data Structure and Algorithms HashingData Structure and Algorithms Hashing
Data Structure and Algorithms Hashing
 
Minimum spanning tree
Minimum spanning treeMinimum spanning tree
Minimum spanning tree
 
Bellman ford algorithm
Bellman ford algorithmBellman ford algorithm
Bellman ford algorithm
 
Optimal binary search tree dynamic programming
Optimal binary search tree   dynamic programmingOptimal binary search tree   dynamic programming
Optimal binary search tree dynamic programming
 
Graphs data structures
Graphs data structuresGraphs data structures
Graphs data structures
 
Threaded binarytree&heapsort
Threaded binarytree&heapsortThreaded binarytree&heapsort
Threaded binarytree&heapsort
 
Spanning trees
Spanning treesSpanning trees
Spanning trees
 
Applications of graphs
Applications of graphsApplications of graphs
Applications of graphs
 
Chap 7 binary threaded tree
Chap 7 binary threaded treeChap 7 binary threaded tree
Chap 7 binary threaded tree
 
Presentation on binary search, quick sort, merge sort and problems
Presentation on binary search, quick sort, merge sort  and problemsPresentation on binary search, quick sort, merge sort  and problems
Presentation on binary search, quick sort, merge sort and problems
 
B+ trees and height balance tree
B+ trees and height balance treeB+ trees and height balance tree
B+ trees and height balance tree
 
Prims and kruskal algorithms
Prims and kruskal algorithmsPrims and kruskal algorithms
Prims and kruskal algorithms
 
Dijkstra algorithm a dynammic programming approach
Dijkstra algorithm   a dynammic programming approachDijkstra algorithm   a dynammic programming approach
Dijkstra algorithm a dynammic programming approach
 
Hash table
Hash tableHash table
Hash table
 
DFS and BFS
DFS and BFSDFS and BFS
DFS and BFS
 

Similar a Graphs (20)

Graphs in data structures
Graphs in data structuresGraphs in data structures
Graphs in data structures
 
Graphs
GraphsGraphs
Graphs
 
Algorithms and data Chapter 3 V Graph.pptx
Algorithms and data Chapter 3 V Graph.pptxAlgorithms and data Chapter 3 V Graph.pptx
Algorithms and data Chapter 3 V Graph.pptx
 
LEC 12-DSALGO-GRAPHS(final12).pdf
LEC 12-DSALGO-GRAPHS(final12).pdfLEC 12-DSALGO-GRAPHS(final12).pdf
LEC 12-DSALGO-GRAPHS(final12).pdf
 
Lecture13
Lecture13Lecture13
Lecture13
 
Topological Sort
Topological SortTopological Sort
Topological Sort
 
Ppt 1
Ppt 1Ppt 1
Ppt 1
 
Analysis &amp; design of algorithm
Analysis &amp; design of algorithmAnalysis &amp; design of algorithm
Analysis &amp; design of algorithm
 
Graph Theory Introduction
Graph Theory IntroductionGraph Theory Introduction
Graph Theory Introduction
 
Unit 9 graph
Unit   9 graphUnit   9 graph
Unit 9 graph
 
Unit-6 Graph.ppsx ppt
Unit-6 Graph.ppsx                                       pptUnit-6 Graph.ppsx                                       ppt
Unit-6 Graph.ppsx ppt
 
Unit ix graph
Unit   ix    graph Unit   ix    graph
Unit ix graph
 
graphin-c1.pnggraphin-c1.txt1 22 3 83 44 5.docx
graphin-c1.pnggraphin-c1.txt1 22 3 83 44 5.docxgraphin-c1.pnggraphin-c1.txt1 22 3 83 44 5.docx
graphin-c1.pnggraphin-c1.txt1 22 3 83 44 5.docx
 
ppt 1.pptx
ppt 1.pptxppt 1.pptx
ppt 1.pptx
 
Unit V - ppt.pptx
Unit V - ppt.pptxUnit V - ppt.pptx
Unit V - ppt.pptx
 
Unit II_Graph.pptxkgjrekjgiojtoiejhgnltegjte
Unit II_Graph.pptxkgjrekjgiojtoiejhgnltegjteUnit II_Graph.pptxkgjrekjgiojtoiejhgnltegjte
Unit II_Graph.pptxkgjrekjgiojtoiejhgnltegjte
 
Graph 1
Graph 1Graph 1
Graph 1
 
Graph
GraphGraph
Graph
 
Talk on Graph Theory - I
Talk on Graph Theory - ITalk on Graph Theory - I
Talk on Graph Theory - I
 
Graph_data_structure_information_engineering.pptx
Graph_data_structure_information_engineering.pptxGraph_data_structure_information_engineering.pptx
Graph_data_structure_information_engineering.pptx
 

Más de Lakshmi Sarvani Videla (20)

Data Science Using Python
Data Science Using PythonData Science Using Python
Data Science Using Python
 
Programs on multithreading
Programs on multithreadingPrograms on multithreading
Programs on multithreading
 
Menu Driven programs in Java
Menu Driven programs in JavaMenu Driven programs in Java
Menu Driven programs in Java
 
Recursion in C
Recursion in CRecursion in C
Recursion in C
 
Simple questions on structures concept
Simple questions on structures conceptSimple questions on structures concept
Simple questions on structures concept
 
Errors incompetitiveprogramming
Errors incompetitiveprogrammingErrors incompetitiveprogramming
Errors incompetitiveprogramming
 
Relational Operators in C
Relational Operators in CRelational Operators in C
Relational Operators in C
 
Recursive functions in C
Recursive functions in CRecursive functions in C
Recursive functions in C
 
Function Pointer in C
Function Pointer in CFunction Pointer in C
Function Pointer in C
 
Functions
FunctionsFunctions
Functions
 
Java sessionnotes
Java sessionnotesJava sessionnotes
Java sessionnotes
 
Singlelinked list
Singlelinked listSinglelinked list
Singlelinked list
 
B trees
B treesB trees
B trees
 
Functions in python3
Functions in python3Functions in python3
Functions in python3
 
Dictionary
DictionaryDictionary
Dictionary
 
Sets
SetsSets
Sets
 
Lists
ListsLists
Lists
 
DataStructures notes
DataStructures notesDataStructures notes
DataStructures notes
 
Solutionsfor co2 C Programs for data structures
Solutionsfor co2 C Programs for data structuresSolutionsfor co2 C Programs for data structures
Solutionsfor co2 C Programs for data structures
 
C programs
C programsC programs
C programs
 

Último

Repurposing LNG terminals for Hydrogen Ammonia: Feasibility and Cost Saving
Repurposing LNG terminals for Hydrogen Ammonia: Feasibility and Cost SavingRepurposing LNG terminals for Hydrogen Ammonia: Feasibility and Cost Saving
Repurposing LNG terminals for Hydrogen Ammonia: Feasibility and Cost SavingEdi Saputra
 
Artificial Intelligence Chap.5 : Uncertainty
Artificial Intelligence Chap.5 : UncertaintyArtificial Intelligence Chap.5 : Uncertainty
Artificial Intelligence Chap.5 : UncertaintyKhushali Kathiriya
 
Apidays New York 2024 - The value of a flexible API Management solution for O...
Apidays New York 2024 - The value of a flexible API Management solution for O...Apidays New York 2024 - The value of a flexible API Management solution for O...
Apidays New York 2024 - The value of a flexible API Management solution for O...apidays
 
Cloud Frontiers: A Deep Dive into Serverless Spatial Data and FME
Cloud Frontiers:  A Deep Dive into Serverless Spatial Data and FMECloud Frontiers:  A Deep Dive into Serverless Spatial Data and FME
Cloud Frontiers: A Deep Dive into Serverless Spatial Data and FMESafe Software
 
DEV meet-up UiPath Document Understanding May 7 2024 Amsterdam
DEV meet-up UiPath Document Understanding May 7 2024 AmsterdamDEV meet-up UiPath Document Understanding May 7 2024 Amsterdam
DEV meet-up UiPath Document Understanding May 7 2024 AmsterdamUiPathCommunity
 
"I see eyes in my soup": How Delivery Hero implemented the safety system for ...
"I see eyes in my soup": How Delivery Hero implemented the safety system for ..."I see eyes in my soup": How Delivery Hero implemented the safety system for ...
"I see eyes in my soup": How Delivery Hero implemented the safety system for ...Zilliz
 
Strategies for Landing an Oracle DBA Job as a Fresher
Strategies for Landing an Oracle DBA Job as a FresherStrategies for Landing an Oracle DBA Job as a Fresher
Strategies for Landing an Oracle DBA Job as a FresherRemote DBA Services
 
EMPOWERMENT TECHNOLOGY GRADE 11 QUARTER 2 REVIEWER
EMPOWERMENT TECHNOLOGY GRADE 11 QUARTER 2 REVIEWEREMPOWERMENT TECHNOLOGY GRADE 11 QUARTER 2 REVIEWER
EMPOWERMENT TECHNOLOGY GRADE 11 QUARTER 2 REVIEWERMadyBayot
 
Finding Java's Hidden Performance Traps @ DevoxxUK 2024
Finding Java's Hidden Performance Traps @ DevoxxUK 2024Finding Java's Hidden Performance Traps @ DevoxxUK 2024
Finding Java's Hidden Performance Traps @ DevoxxUK 2024Victor Rentea
 
WSO2's API Vision: Unifying Control, Empowering Developers
WSO2's API Vision: Unifying Control, Empowering DevelopersWSO2's API Vision: Unifying Control, Empowering Developers
WSO2's API Vision: Unifying Control, Empowering DevelopersWSO2
 
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...Connector Corner: Accelerate revenue generation using UiPath API-centric busi...
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...DianaGray10
 
Introduction to Multilingual Retrieval Augmented Generation (RAG)
Introduction to Multilingual Retrieval Augmented Generation (RAG)Introduction to Multilingual Retrieval Augmented Generation (RAG)
Introduction to Multilingual Retrieval Augmented Generation (RAG)Zilliz
 
Corporate and higher education May webinar.pptx
Corporate and higher education May webinar.pptxCorporate and higher education May webinar.pptx
Corporate and higher education May webinar.pptxRustici Software
 
Elevate Developer Efficiency & build GenAI Application with Amazon Q​
Elevate Developer Efficiency & build GenAI Application with Amazon Q​Elevate Developer Efficiency & build GenAI Application with Amazon Q​
Elevate Developer Efficiency & build GenAI Application with Amazon Q​Bhuvaneswari Subramani
 
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, AdobeApidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobeapidays
 
ICT role in 21st century education and its challenges
ICT role in 21st century education and its challengesICT role in 21st century education and its challenges
ICT role in 21st century education and its challengesrafiqahmad00786416
 
presentation ICT roal in 21st century education
presentation ICT roal in 21st century educationpresentation ICT roal in 21st century education
presentation ICT roal in 21st century educationjfdjdjcjdnsjd
 
CNIC Information System with Pakdata Cf In Pakistan
CNIC Information System with Pakdata Cf In PakistanCNIC Information System with Pakdata Cf In Pakistan
CNIC Information System with Pakdata Cf In Pakistandanishmna97
 

Último (20)

Repurposing LNG terminals for Hydrogen Ammonia: Feasibility and Cost Saving
Repurposing LNG terminals for Hydrogen Ammonia: Feasibility and Cost SavingRepurposing LNG terminals for Hydrogen Ammonia: Feasibility and Cost Saving
Repurposing LNG terminals for Hydrogen Ammonia: Feasibility and Cost Saving
 
Artificial Intelligence Chap.5 : Uncertainty
Artificial Intelligence Chap.5 : UncertaintyArtificial Intelligence Chap.5 : Uncertainty
Artificial Intelligence Chap.5 : Uncertainty
 
Apidays New York 2024 - The value of a flexible API Management solution for O...
Apidays New York 2024 - The value of a flexible API Management solution for O...Apidays New York 2024 - The value of a flexible API Management solution for O...
Apidays New York 2024 - The value of a flexible API Management solution for O...
 
Cloud Frontiers: A Deep Dive into Serverless Spatial Data and FME
Cloud Frontiers:  A Deep Dive into Serverless Spatial Data and FMECloud Frontiers:  A Deep Dive into Serverless Spatial Data and FME
Cloud Frontiers: A Deep Dive into Serverless Spatial Data and FME
 
Understanding the FAA Part 107 License ..
Understanding the FAA Part 107 License ..Understanding the FAA Part 107 License ..
Understanding the FAA Part 107 License ..
 
DEV meet-up UiPath Document Understanding May 7 2024 Amsterdam
DEV meet-up UiPath Document Understanding May 7 2024 AmsterdamDEV meet-up UiPath Document Understanding May 7 2024 Amsterdam
DEV meet-up UiPath Document Understanding May 7 2024 Amsterdam
 
"I see eyes in my soup": How Delivery Hero implemented the safety system for ...
"I see eyes in my soup": How Delivery Hero implemented the safety system for ..."I see eyes in my soup": How Delivery Hero implemented the safety system for ...
"I see eyes in my soup": How Delivery Hero implemented the safety system for ...
 
Strategies for Landing an Oracle DBA Job as a Fresher
Strategies for Landing an Oracle DBA Job as a FresherStrategies for Landing an Oracle DBA Job as a Fresher
Strategies for Landing an Oracle DBA Job as a Fresher
 
EMPOWERMENT TECHNOLOGY GRADE 11 QUARTER 2 REVIEWER
EMPOWERMENT TECHNOLOGY GRADE 11 QUARTER 2 REVIEWEREMPOWERMENT TECHNOLOGY GRADE 11 QUARTER 2 REVIEWER
EMPOWERMENT TECHNOLOGY GRADE 11 QUARTER 2 REVIEWER
 
Finding Java's Hidden Performance Traps @ DevoxxUK 2024
Finding Java's Hidden Performance Traps @ DevoxxUK 2024Finding Java's Hidden Performance Traps @ DevoxxUK 2024
Finding Java's Hidden Performance Traps @ DevoxxUK 2024
 
WSO2's API Vision: Unifying Control, Empowering Developers
WSO2's API Vision: Unifying Control, Empowering DevelopersWSO2's API Vision: Unifying Control, Empowering Developers
WSO2's API Vision: Unifying Control, Empowering Developers
 
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...Connector Corner: Accelerate revenue generation using UiPath API-centric busi...
Connector Corner: Accelerate revenue generation using UiPath API-centric busi...
 
Introduction to Multilingual Retrieval Augmented Generation (RAG)
Introduction to Multilingual Retrieval Augmented Generation (RAG)Introduction to Multilingual Retrieval Augmented Generation (RAG)
Introduction to Multilingual Retrieval Augmented Generation (RAG)
 
Corporate and higher education May webinar.pptx
Corporate and higher education May webinar.pptxCorporate and higher education May webinar.pptx
Corporate and higher education May webinar.pptx
 
Elevate Developer Efficiency & build GenAI Application with Amazon Q​
Elevate Developer Efficiency & build GenAI Application with Amazon Q​Elevate Developer Efficiency & build GenAI Application with Amazon Q​
Elevate Developer Efficiency & build GenAI Application with Amazon Q​
 
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, AdobeApidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
Apidays New York 2024 - Scaling API-first by Ian Reasor and Radu Cotescu, Adobe
 
+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...
+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...
+971581248768>> SAFE AND ORIGINAL ABORTION PILLS FOR SALE IN DUBAI AND ABUDHA...
 
ICT role in 21st century education and its challenges
ICT role in 21st century education and its challengesICT role in 21st century education and its challenges
ICT role in 21st century education and its challenges
 
presentation ICT roal in 21st century education
presentation ICT roal in 21st century educationpresentation ICT roal in 21st century education
presentation ICT roal in 21st century education
 
CNIC Information System with Pakdata Cf In Pakistan
CNIC Information System with Pakdata Cf In PakistanCNIC Information System with Pakdata Cf In Pakistan
CNIC Information System with Pakdata Cf In Pakistan
 

Graphs