Lamport’s Logical Clock was created by Leslie Lamport. It is a procedure to determine the order of events occurring. It provides a basis for the more advanced Vector Clock Algorithm. Due to the absence of a Global Clock in a Distributed Operating System Lamport Logical Clock is needed.
Algorithm:
- Happened before relation(->): a -> b, means ‘a’ happened before ‘b’.
-
Logical Clock: The criteria for the logical clocks are:
- [C1]: Ci (a) < Ci(b), [ Ci -> Logical Clock, If ‘a’ happened before ‘b’, then time of ‘a’ will be less than ‘b’ in a particular process. ]
- [C2]: Ci(a) < Cj(b), [ Clock value of Ci(a) is less than Cj(b) ]
Reference:
- Process: Pi
- Event: Eij, where i is the process in number and j: jth event in the ith process.
- tm: vector time span for message m.
- Ci vector clock associated with process Pi, the jth element is Ci[j] and contains Pi‘s latest value for the current time in process Pj.
- d: drift time, generally d is 1.
Implementation Rules[IR]:
- [IR1]: If a -> b [‘a’ happened before ‘b’ within the same process] then, Ci(b) =Ci(a) + d
- [IR2]: Cj = max(Cj, tm + d) [If there’s more number of processes, then tm = value of Ci(a), Cj = max value between Cj and tm + d]
For Example:
-
Take the starting value as 1, since it is the 1st event and there is no incoming value at the starting point:
- e11 = 1
- e21 = 1
-
The value of the next point will go on increasing by d (d = 1), if there is no incoming value i.e., to follow [IR1].
- e12 = e11 + d = 1 + 1 = 2
- e13 = e12 + d = 2 + 1 = 3
- e14 = e13 + d = 3 + 1 = 4
- e15 = e14 + d = 4 + 1 = 5
- e16 = e15 + d = 5 + 1 = 6
- e22 = e21 + d = 1 + 1 = 2
- e24 = e23 + d = 3 + 1 = 4
- e26 = e25 + d = 6 + 1 = 7
-
When there will be incoming value, then follow [IR2] i.e., take the maximum value between Cj and Tm + d.
- e17 = max(7, 5) = 7, [e16 + d = 6 + 1 = 7, e24 + d = 4 + 1 = 5, maximum among 7 and 5 is 7]
- e23 = max(3, 3) = 3, [e22 + d = 2 + 1 = 3, e12 + d = 2 + 1 = 3, maximum among 3 and 3 is 3]
- e25 = max(5, 6) = 6, [e24 + 1 = 4 + 1 = 5, e15 + d = 5 + 1 = 6, maximum among 5 and 6 is 6]
Limitation:
- In case of [IR1], if a -> b, then C(a) < C(b) -> true.
- In case of [IR2], if a -> b, then C(a) < C(b) -> May be true or may not be true.
Below is the C program to implement Lamport’s Logical Clock:
C++
// C++ program to illustrate the Lamport's // Logical Clock #include <bits/stdc++.h> using namespace std;
// Function to find the maximum timestamp // between 2 events int max1( int a, int b)
{ // Return the greatest of the two
if (a > b)
return a;
else
return b;
} // Function to display the logical timestamp void display( int e1, int e2,
int p1[5], int p2[3])
{ int i;
cout << "\nThe time stamps of "
"events in P1:\n" ;
for (i = 0; i < e1; i++) {
cout << p1[i] << " " ;
}
cout << "\nThe time stamps of "
"events in P2:\n" ;
// Print the array p2[]
for (i = 0; i < e2; i++)
cout << p2[i] << " " ;
} // Function to find the timestamp of events void lamportLogicalClock( int e1, int e2,
int m[5][3])
{ int i, j, k, p1[e1], p2[e2];
// Initialize p1[] and p2[]
for (i = 0; i < e1; i++)
p1[i] = i + 1;
for (i = 0; i < e2; i++)
p2[i] = i + 1;
cout << "\t" ;
for (i = 0; i < e2; i++)
cout << "\te2" << i + 1;
for (i = 0; i < e1; i++) {
cout << "\n e1" << i + 1 << "\t" ;
for (j = 0; j < e2; j++)
cout << m[i][j] << "\t" ;
}
for (i = 0; i < e1; i++) {
for (j = 0; j < e2; j++) {
// Change the timestamp if the
// message is sent
if (m[i][j] == 1) {
p2[j] = max1(p2[j], p1[i] + 1);
for (k = j + 1; k < e2; k++)
p2[k] = p2[k - 1] + 1;
}
// Change the timestamp if the
// message is received
if (m[i][j] == -1) {
p1[i] = max1(p1[i], p2[j] + 1);
for (k = i + 1; k < e1; k++)
p1[k] = p1[k - 1] + 1;
}
}
}
// Function Call
display(e1, e2, p1, p2);
} // Driver Code int main()
{ int e1 = 5, e2 = 3, m[5][3];
// message is sent and received
// between two process
/*dep[i][j] = 1, if message is sent
from ei to ej
dep[i][j] = -1, if message is received
by ei from ej
dep[i][j] = 0, otherwise*/
m[0][0] = 0;
m[0][1] = 0;
m[0][2] = 0;
m[1][0] = 0;
m[1][1] = 0;
m[1][2] = 1;
m[2][0] = 0;
m[2][1] = 0;
m[2][2] = 0;
m[3][0] = 0;
m[3][1] = 0;
m[3][2] = 0;
m[4][0] = 0;
m[4][1] = -1;
m[4][2] = 0;
// Function Call
lamportLogicalClock(e1, e2, m);
return 0;
} |
C
// C program to illustrate the Lamport's // Logical Clock #include <stdio.h> // Function to find the maximum timestamp // between 2 events int max1( int a, int b)
{ // Return the greatest of the two
if (a > b)
return a;
else
return b;
} // Function to display the logical timestamp void display( int e1, int e2,
int p1[5], int p2[3])
{ int i;
printf ( "\nThe time stamps of "
"events in P1:\n" );
for (i = 0; i < e1; i++) {
printf ( "%d " , p1[i]);
}
printf ( "\nThe time stamps of "
"events in P2:\n" );
// Print the array p2[]
for (i = 0; i < e2; i++)
printf ( "%d " , p2[i]);
} // Function to find the timestamp of events void lamportLogicalClock( int e1, int e2,
int m[5][3])
{ int i, j, k, p1[e1], p2[e2];
// Initialize p1[] and p2[]
for (i = 0; i < e1; i++)
p1[i] = i + 1;
for (i = 0; i < e2; i++)
p2[i] = i + 1;
for (i = 0; i < e2; i++)
printf ( "\te2%d" , i + 1);
for (i = 0; i < e1; i++) {
printf ( "\n e1%d \t" , i + 1);
for (j = 0; j < e2; j++)
printf ( "%d\t" , m[i][j]);
}
for (i = 0; i < e1; i++) {
for (j = 0; j < e2; j++) {
// Change the timestamp if the
// message is sent
if (m[i][j] == 1) {
p2[j] = max1(p2[j], p1[i] + 1);
for (k = j + 1; k < e2; k++)
p2[k] = p2[k - 1] + 1;
}
// Change the timestamp if the
// message is received
if (m[i][j] == -1) {
p1[i] = max1(p1[i], p2[j] + 1);
for (k = i + 1; k < e1; k++)
p1[k] = p1[k - 1] + 1;
}
}
}
// Function Call
display(e1, e2, p1, p2);
} // Driver Code int main()
{ int e1 = 5, e2 = 3, m[5][3];
// message is sent and received
// between two process
/*dep[i][j] = 1, if message is sent
from ei to ej
dep[i][j] = -1, if message is received
by ei from ej
dep[i][j] = 0, otherwise*/
m[0][0] = 0;
m[0][1] = 0;
m[0][2] = 0;
m[1][0] = 0;
m[1][1] = 0;
m[1][2] = 1;
m[2][0] = 0;
m[2][1] = 0;
m[2][2] = 0;
m[3][0] = 0;
m[3][1] = 0;
m[3][2] = 0;
m[4][0] = 0;
m[4][1] = -1;
m[4][2] = 0;
// Function Call
lamportLogicalClock(e1, e2, m);
return 0;
} |
Java
// Java program to illustrate the Lamport's // Logical Clock import java.util.*;
public class GFG {
// Function to find the maximum timestamp
// between 2 events
static int max1( int a, int b)
{
// Return the greatest of the two
if (a > b)
return a;
else
return b;
}
// Function to display the logical timestamp
static void display( int e1, int e2, int p1[], int p2[])
{
int i;
System.out.print(
"\nThe time stamps of events in P1:\n" );
for (i = 0 ; i < e1; i++) {
System.out.print(p1[i] + " " );
}
System.out.println(
"\nThe time stamps of events in P2:" );
// Print the array p2[]
for (i = 0 ; i < e2; i++)
System.out.print(p2[i] + " " );
}
// Function to find the timestamp of events
static void lamportLogicalClock( int e1, int e2,
int m[][])
{
int i, j, k;
int p1[] = new int [e1];
int p2[] = new int [e2];
// Initialize p1[] and p2[]
for (i = 0 ; i < e1; i++)
p1[i] = i + 1 ;
for (i = 0 ; i < e2; i++)
p2[i] = i + 1 ;
for (i = 0 ; i < e2; i++)
System.out.print( "\te2" + (i + 1 ));
for (i = 0 ; i < e1; i++) {
System.out.print( "\n e1" + (i + 1 ) + "\t" );
for (j = 0 ; j < e2; j++)
System.out.print(m[i][j] + "\t" );
}
for (i = 0 ; i < e1; i++) {
for (j = 0 ; j < e2; j++) {
// Change the timestamp if the
// message is sent
if (m[i][j] == 1 ) {
p2[j] = max1(p2[j], p1[i] + 1 );
for (k = j + 1 ; k < e2; k++)
p2[k] = p2[k - 1 ] + 1 ;
}
// Change the timestamp if the
// message is received
if (m[i][j] == - 1 ) {
p1[i] = max1(p1[i], p2[j] + 1 );
for (k = i + 1 ; k < e1; k++)
p1[k] = p1[k - 1 ] + 1 ;
}
}
}
// Function Call
display(e1, e2, p1, p2);
}
public static void main(String args[])
{
int e1 = 5 , e2 = 3 ;
int m[][] = new int [ 5 ][ 3 ];
// message is sent and received
// between two process
/*dep[i][j] = 1, if message is sent
from ei to ej
dep[i][j] = -1, if message is received
by ei from ej
dep[i][j] = 0, otherwise*/
m[ 0 ][ 0 ] = 0 ;
m[ 0 ][ 1 ] = 0 ;
m[ 0 ][ 2 ] = 0 ;
m[ 1 ][ 0 ] = 0 ;
m[ 1 ][ 1 ] = 0 ;
m[ 1 ][ 2 ] = 1 ;
m[ 2 ][ 0 ] = 0 ;
m[ 2 ][ 1 ] = 0 ;
m[ 2 ][ 2 ] = 0 ;
m[ 3 ][ 0 ] = 0 ;
m[ 3 ][ 1 ] = 0 ;
m[ 3 ][ 2 ] = 0 ;
m[ 4 ][ 0 ] = 0 ;
m[ 4 ][ 1 ] = - 1 ;
m[ 4 ][ 2 ] = 0 ;
// Function Call
lamportLogicalClock(e1, e2, m);
}
} // This code is contributed by nmkiniqw7b |
Python3
# Python program to illustrate the Lamport's # Logical Clock # Function to find the maximum timestamp # between 2 events def max1(a, b) :
# Return the greatest of the two
if a > b :
return a
else :
return b
# Function to display the logical timestamp def display(e1, e2, p1, p2) :
print ()
print ( "The time stamps of events in P1:" )
for i in range ( 0 , e1) :
print (p1[i], end = " " )
print ()
print ( "The time stamps of events in P2:" )
# Print the array p2[]
for i in range ( 0 , e2) :
print (p2[i], end = " " )
# Function to find the timestamp of events def lamportLogicalClock(e1, e2, m) :
p1 = [ 0 ] * e1
p2 = [ 0 ] * e2
# Initialize p1[] and p2[]
for i in range ( 0 , e1) :
p1[i] = i + 1
for i in range ( 0 , e2) :
p2[i] = i + 1
for i in range ( 0 , e2) :
print (end = '\t' )
print ( "e2" , end = "")
print (i + 1 , end = "")
for i in range ( 0 , e1) :
print ()
print ( "e1" , end = "")
print (i + 1 , end = "\t" )
for j in range ( 0 , e2) :
print (m[i][j], end = "\t" )
for i in range ( 0 , e1) :
for j in range ( 0 , e2) :
# Change the timestamp if the
# message is sent
if (m[i][j] = = 1 ) :
p2[j] = max1(p2[j], p1[i] + 1 )
for i in range (j + 1 , e2) :
p2[k] = p2[k - 1 ] + 1
# Change the timestamp if the
# message is received
if (m[i][j] = = - 1 ) :
p1[i] = max1(p1[i], p2[j] + 1 )
for k in range (i + 1 , e1) :
p1[k] = p1[k - 1 ] + 1
# Function Call
display(e1, e2, p1, p2)
# Driver Code if __name__ = = "__main__" :
e1 = 5
e2 = 3
m = [[ 0 ] * 3 for i in range ( 0 , 5 )]
# dep[i][j] = 1, if message is sent
# from ei to ej
# dep[i][j] = -1, if message is received
# by ei from ej
# dep[i][j] = 0, otherwise
m[ 0 ][ 0 ] = 0
m[ 0 ][ 1 ] = 0
m[ 0 ][ 2 ] = 0
m[ 1 ][ 0 ] = 0
m[ 1 ][ 1 ] = 0
m[ 1 ][ 2 ] = 1
m[ 2 ][ 0 ] = 0
m[ 2 ][ 1 ] = 0
m[ 2 ][ 2 ] = 0
m[ 3 ][ 0 ] = 0
m[ 3 ][ 1 ] = 0
m[ 3 ][ 2 ] = 0
m[ 4 ][ 0 ] = 0
m[ 4 ][ 1 ] = - 1
m[ 4 ][ 2 ] = 0
# Function Call
lamportLogicalClock(e1, e2, m)
# This code is contributed by rakeshsahni
|
C#
// C# program to illustrate the Lamport's // Logical Clock using System;
public class GFG {
// Function to find the maximum timestamp
// between 2 events
static int max1( int a, int b)
{
// Return the greatest of the two
if (a > b)
return a;
else
return b;
}
// Function to display the logical timestamp
static void display( int e1, int e2, int [] p1, int [] p2)
{
int i;
Console.Write(
"\nThe time stamps of events in P1:\n" );
for (i = 0; i < e1; i++) {
Console.Write(p1[i] + " " );
}
Console.WriteLine(
"\nThe time stamps of events in P2:" );
// Print the array p2[]
for (i = 0; i < e2; i++)
Console.Write(p2[i] + " " );
}
// Function to find the timestamp of events
static void lamportLogicalClock( int e1, int e2,
int [, ] m)
{
int i, j, k;
int [] p1 = new int [e1];
int [] p2 = new int [e2];
// Initialize p1[] and p2[]
for (i = 0; i < e1; i++)
p1[i] = i + 1;
for (i = 0; i < e2; i++)
p2[i] = i + 1;
for (i = 0; i < e2; i++)
Console.Write( "\te2" + (i + 1));
for (i = 0; i < e1; i++) {
Console.Write( "\n e1" + (i + 1) + "\t" );
for (j = 0; j < e2; j++)
Console.Write(m[i, j] + "\t" );
}
for (i = 0; i < e1; i++) {
for (j = 0; j < e2; j++) {
// Change the timestamp if the
// message is sent
if (m[i, j] == 1) {
p2[j] = max1(p2[j], p1[i] + 1);
for (k = j + 1; k < e2; k++)
p2[k] = p2[k - 1] + 1;
}
// Change the timestamp if the
// message is received
if (m[i, j] == -1) {
p1[i] = max1(p1[i], p2[j] + 1);
for (k = i + 1; k < e1; k++)
p1[k] = p1[k - 1] + 1;
}
}
}
// Function Call
display(e1, e2, p1, p2);
}
static public void Main()
{
// Code
int e1 = 5, e2 = 3;
int [, ] m = new int [5, 3];
// message is sent and received
// between two process
/*dep[i][j] = 1, if message is sent
from ei to ej
dep[i][j] = -1, if message is received
by ei from ej
dep[i][j] = 0, otherwise*/
m[0, 0] = 0;
m[0, 1] = 0;
m[0, 2] = 0;
m[1, 0] = 0;
m[1, 1] = 0;
m[1, 2] = 1;
m[2, 0] = 0;
m[2, 1] = 0;
m[2, 2] = 0;
m[3, 0] = 0;
m[3, 1] = 0;
m[3, 2] = 0;
m[4, 0] = 0;
m[4, 1] = -1;
m[4, 2] = 0;
// Function Call
lamportLogicalClock(e1, e2, m);
}
} // This code is contributed by lokeshmvs21. |
Javascript
<script> // JavaScript program to illustrate the Lamport's
// Logical Clock
// Function to find the maximum timestamp
// between 2 events
const max1 = (a, b) => {
// Return the greatest of the two
if (a > b)
return a;
else
return b;
}
// Function to display the logical timestamp
const display = (e1, e2, p1, p2) => {
let i;
document.write(`<br/>The time stamps of events in P1:<br/>`);
for (i = 0; i < e1; i++) {
document.write(`${p1[i]} `);
}
document.write(`<br/>The time stamps of events in P2:<br/>`);
// Print the array p2[]
for (i = 0; i < e2; i++)
document.write(`${p2[i]} `);
}
// Function to find the timestamp of events
const lamportLogicalClock = (e1, e2, m) => {
let i, j, k, p1 = [], p2 = [];
// Initialize p1[] and p2[]
for (i = 0; i < e1; i++)
p1[i] = i + 1;
for (i = 0; i < e2; i++)
p2[i] = i + 1;
for (i = 0; i < e2; i++)
document.write(`\te2${i + 1}`)
for (i = 0; i < e1; i++) {
document.write(`<br/>e1${i + 1} `)
for (j = 0; j < e2; j++)
document.write(`${m[i][j]}\t`);
}
for (i = 0; i < e1; i++) {
for (j = 0; j < e2; j++) {
// Change the timestamp if the
// message is sent
if (m[i][j] == 1) {
p2[j] = max1(p2[j], p1[i] + 1);
for (k = j + 1; k < e2; k++)
p2[k] = p2[k - 1] + 1;
}
// Change the timestamp if the
// message is received
if (m[i][j] == -1) {
p1[i] = max1(p1[i], p2[j] + 1);
for (k = i + 1; k < e1; k++)
p1[k] = p1[k - 1] + 1;
}
}
}
// Function Call
display(e1, e2, p1, p2);
}
// Driver Code
let e1 = 5, e2 = 3;
// message is sent and received
// between two process
/*dep[i][j] = 1, if message is sent
from ei to ej
dep[i][j] = -1, if message is received
by ei from ej
dep[i][j] = 0, otherwise*/
const m = [
[0, 0, 0],
[0, 0, 1],
[0, 0, 0],
[0, 0, 0],
[0, -1, 0]
]
// Function Call
lamportLogicalClock(e1, e2, m);
// This code is contributed by rakeshsahni </script> |
Output
e21 e22 e23 e11 0 0 0 e12 0 0 1 e13 0 0 0 e14 0 0 0 e15 0 -1 0 The time stamps of events in P1: 1 2 3 4 5 The time stamps of events in P2: 1 2 3
Time Complexity: O(e1 * e2 * (e1 + e2))
Auxiliary Space: O(e1 + e2)