The document describes MapReduce, a programming model for processing large datasets in a distributed computing environment. It explains the map and reduce functions, providing examples of doubling array elements with map and summing array elements with reduce. General forms are given for map and reduce, showing how arbitrary functions can be passed to each. Benefits are that code only needs to replace the map and reduce implementations rather than be rewritten when run on multiple machines. Hadoop is introduced as an implementation of MapReduce that is parallel, distributed, fault-tolerant and aware of network topology.

1. Map Reduce

2. Map

3. Double the contents of an array
var a = [1, 2, 3];
for (int I = 0; I < a.length; i++){
a[ i ] = 2*a[ i ];
}
Output:
a = [2, 4, 6];

4. Double the contents of an array
var a = [1, 2, 3];
for (int i = 0; i < a.length; i++){
a[ i ] = 2*a[ i ];
}
var a = [1, 2, 3];
for (int i = 0; i < a.length; i++){
a[ i ] = fn(a[ i ]);
}
where fn(x){ return 2*x;}

5. Double the contents of an array
var a = [1, 2, 3];
for (int i = 0; i < a.length; i++){
a[ i ] = fn(a[ i ]);
}
where fn(x){ return 2*x;}
function map(fn, a){
for (int i = 0; i < a.length; i++){
a[ i ] = fn(a[ i ]);
}
where fn(x){ return 2*x;}

6. Double the contents of an array
function map(fn, a){
for (int i = 0; i < a.length; i++){
a[ i ] = fn(a[ i ]);
}
where fn(x){ return 2*x;}
map(function(x){ return 2*x;},a}
General Form

7. Reduce

8. Sum the contents of an array
function sum(a){
var s= 0;
for(int i=0; i<a.length; i++){
s = s + a[ i ];
}
return s;
}

9. Sum the contents of an array
function sum(a){
var s= 0;
for(int i=0; i<a.length; i++){
s = s + a[ I ];
}
return s;
} function sum(a){
var s= 0;
for(int i=0; i<a.length; i++){
s = fn(s, a[ I ]);
}
return s;
}
where fn(a, b){ return a+b;}

10. Sum the contents of an array
function sum(a){
var s= 0;
for(int i=0; i<a.length; i++){
s = fn(s, a[ I ]);
}
return s;
}
where fn(a, b){ return a+b;}
function reduce(fn, a, init){
var s= init;
for(int i=0; i<a.length; i++){
s = fn(s, a[ I ]);
}
return s;
}
where fn(a, b){ return a+b;}

11. Sum the contents of an array
function reduce(fn, a, init){
var s= init;
for(int i=0; i<a.length; i++){
s = fn(s, a[ I ]);
}
return s;
} where fn(a, b){ return a+b;}
General form
reduce(function(a,b){ retun a+b;}, a, init);

12. Benefits
 In case of big arrays, code running on
multiple machines, one need not to rewrite
the code for computing but just replace the
implementation of map and reduce as
required.
Microsoft Word
Document
map(function(x){ return 2*x;},a}
reduce(function(a,b){ return a+b;}, a, init);

13. What is hadoop?
 Hadoop is parallel, distributive, fault
tolerant and network topology aware
implementation of MapReduce algorithm.