/ 
GRID-Cluster-0.04
River stage zero No dependents
/ GRID::Cluster::Tutorial

NAME

GRID::Cluster::Tutorial - An introduction to parallel computing using components

SYNOPSIS

$ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 1
Calculating Pi with 1000000000 iterations and 1 processes
Elapsed Time: 56.591251 seconds
Pi Value: 3.141593

real    0m58.374s
user    0m0.520s
sys     0m0.048s

$ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 2
Calculating Pi with 1000000000 iterations and 2 processes
Elapsed Time: 28.459958 seconds
Pi Value: 3.141592

real    0m30.610s
user    0m0.524s
sys     0m0.056s

$ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 3
Calculating Pi with 1000000000 iterations and 3 processes
Elapsed Time: 20.956588 seconds
Pi Value: 3.141594

real    0m22.549s
user    0m0.296s
sys     0m0.068s

$ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 6
Calculating Pi with 1000000000 iterations and 6 processes
Elapsed Time: 15.694753 seconds
Pi Value: 3.141594

real    0m17.285s
user    0m0.304s
sys     0m0.104s

$ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 12
Calculating Pi with 1000000000 iterations and 12 processes
Elapsed Time: 13.246352 seconds
Pi Value: 3.141588

real    0m14.798s
user    0m0.328s
sys     0m0.116s

$ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 15
Calculating Pi with 1000000000 iterations and 15 processes
Elapsed Time: 12.924256 seconds
Pi Value: 3.1416

real    0m14.500s
user    0m0.372s
sys     0m0.108s

SUMMARY

Programming is difficult. Parallel programming is harder. As a rule of thumb, 20% of the code is responsible for 80% of the computing time. As anyone working in High Performance Computing knows, optimizing the computing time and optimizing programmer's time are contradictory goals. Therefore, the Pareto Principle applies when considering the total benefits of optimizing: We must find a compromise between the efforts and costs of the High Performance Computing component (HPC) versus the High Performance Programming component (HPP). Another spoke in the Parallel Computing wheel is the need of staff for the set-up, administration and maintenance of the available computer networks. These requirements make difficult the exploitation of distributed systems, specially when several organizations are engaged.

This work explores the convenience of using dynamic languages (like Ruby, Perl or Python) as coordination languages for components written using different HPC tools. The very high programming level provided by these languages make feasible a 'zero administration' setup of a cluster while the use of HPC languages contributes to preserve highest levels of performance. Results show that the overwhelming gain in programmer's time does not implies any loss of performance.

REQUIREMENTS

To experiment with the examples in this tutorial you will need at least two Unix machines with SSH, Perl and an installation of the module GRID::Machine from Casiano Rodriguez. If you are not familiar with Perl or Linux this module probably isn't for you. If you are not familiar with SSH, see

BUILDING A PARALLEL VIRTUAL MACHINE

SSH includes the ability to authenticate users using public keys. Instead of authenticating the user with a password, the SSH server on the remote machine will verify a challenge signed by the user's private key against its copy of the user's public key. To achieve this automatic ssh-authentication you have to:

  • Configure each remote machine in a configuration file (man ssh_config). By default, the configuration file is $HOME/.ssh/config. The basic syntax which this script needs is the following:

    Host host_1
HostName myHost1.mydomain.com
User myUser

Host host_2
HostName myHost2.mydomain.com
User anotherUser
.
.
.
Host host_n
HostName myHostn.mydomain.com
User myUser

  • Run the script pki.pl which is included in this distribution. This script allows the generation of public/private key pairs, using the ssh-keygen command. Generated public key is copied to a list of remote machines. Specifically, the public key is added, if not exist, in the file $HOME/.ssh/authorized_keys of each remote machine.

    The basic execution of the command is as follows:

    local.machine$ ./pki.pl [-v] -c host_1,host_2,...host_n

    In this case, a public/private key pair is generated in the local directory $HOME/.ssh/, using the ssh-keygen command, which must be located in some directory included in $PATH. The filenames of the generated public and private keys are grid_cluster_rsa.pub and grid_cluster_rsa, respectively.

    By default, generated keys have the following characteristics:

    • Type: RSA

    • Number of bits: 2048

    • No passphrase

    Once the public/private key pair has been generated, the public key is copied to remote machines specified by the option -c. This option can be used several times to specify sets of machines with the same password to login. In this way, the copy process of the public key to remote machines is easier.

    The behaviour of the script can be modified by the different supported options. For more information, you can execute the script with the option -h.

  • Add a line for each remote machine in the configuration file that specifies the public/private key which is going to be used to authenticate the user.

    Host host_1
HostName myHost1.mydomain.com
User myUser
IdentityFile ~/.ssh/grid_cluster_rsa 

Host host_2
HostName myHost2.mydomain.com
User anotherUser
IdentityFile ~/.ssh/grid_cluster_rsa 
.
.
.
Host host_n
HostName myHostn.mydomain.com
User myUser
IdentityFile ~/.ssh/grid_cluster_rsa

  • Once the public key is installed on remote machines and the configuration file is properly written, you should be able to authenticate using your private key:

    $ ssh host_1
Linux host_1 2.6.15-1-686-smp #2 SMP Mon Mar 6 15:34:50 UTC 2006 i686
Last login: Sat Jul  7 13:34:00 2007 from local.machine
user@host_1:~$

    You can also automatically execute commands in the remote server:

    local.machine$ ssh host_1 uname -a
Linux host_1 2.6.15-1-686-smp #2 SMP Mon Mar 6 15:34:50 UTC 2006 i686 GNU/Linux

A PARALLEL ALGORITHM

The selected case of study for this tutorial is the computation of the number Pi using numerical integration. This is not, in fact, a good way to compute Pi, but makes a good example of how to exploit several machines to fulfill a coordination task.

To obtain the value of the number Pi, the area under the curve 4/(1+x*x) in the interval [0,1] must be computed. To obtain an approximated value of the number Pi, this interval can be divided into N sub-intervals of size 1/N. Adding up the areas of the small rectangles with base 1/N and height the value of the curve 4/(1+x*x) in the middle of the interval, an approximation is obtained. Since the goal is to optimize the execution time, the sum of the areas will be distributed among the processors. Every different process located on remote machines will have assigned a logical identifier numbered from 0 to np-1 (being np the total number of processes) and each machine will sum up the areas of roughly N/np intervals.

To achieve a higher performance the code executed by every process has been written in C language:

 1  #include <stdio.h>
 2  #include <stdlib.h>
 3
 4  main(int argc, char **argv) {
 5    int id, N, np, i;
 6    double sum, left;
 7
 8    if (argc != 4) {
 9      printf("Usage:\n%s id N np\n",argv[0]);
10      exit(1);
11    }
12
13    id = atoi(argv[1]);
14    N  = atoi(argv[2]);
15    np = atoi(argv[3]);
16
17    for(i = id, sum = 0; i < N; i += np) {
18      double x = (i + 0.5) / N;
19      sum += 4 / (1 + x * x);
20    }
21
22    sum /= N;
23    printf("%lf\n", sum);
24    exit(0);
25  }

The program receives three arguments: The first one, id identifies the process with a logical number, the second one, N, is the total number of intervals, the third np is the number of processes being used. Notice the for loop at line 17: Process id sums up the areas corresponding to intervals id, id+np, id+2*np, etc. The program concludes writing to the standard output the partial sum.

Observe that, since infinite precision numbers are not being used, errors introduced by rounding and truncation imply that increasing N would not lead to a more precise evaluation of the number Pi.

COORDINATING A PARALLEL VIRTUAL MACHINE

To coordinate the component program aforementioned, a driver has been written. This driver uses GRID::Cluster and runs a number of copies of the former C program in a set of available machines, adding up partial results as soon as they are available:

1 #!/usr/bin/perl
2 use warnings;
3 use strict;
4 use GRID::Cluster;
5 use Time::HiRes qw(time gettimeofday tv_interval);
6 use Getopt::Long;
7 use List::Util qw(sum);
8 use Pod::Usage;

First lines load the modules:

  • GRID::Cluster will be used to open SSH connections with remote machines and to coordinate the components among different remote processes.

  • Time::HiRes will be used to time the processes.

  • Getopt::Long will be used to obtain command line options of the user.

  • List::Util allows the use of a set of methods to manage lists of elements.

  • Pod::Usage will be used to present the correct usage of the program.

Next lines present the initialization process, where the command line parameters introduced by the user are obtained:

10 my $config = 'MachineConfig.pm';
11 my $np = 1;
12 my $N = 100;
13 my $clean = 0;
14
15 GetOptions(
16   'config=s' => \$config, # Module containing the definition of %machine and %map_id_machine
17   'np=i'     => \$np,
18   'N=i'      => \$N,
19   'clean'    => \$clean,
20   'help'     => sub { pod2usage( -exitval => 0, -verbose => 2,) },
21 ) or pod2usage(-msg => "Bad usage\n", -exitval => 1, -verbose => 1,);
22
23 my ($debug,  $max_num_np) = do $config;
24
25 my @machine = sort { $max_num_np->{$b} <=> $max_num_np->{$a} } keys  %$max_num_np;

At lines 15-21, the function GetOptions obtains the command line parameters introduced by the user and checks if the program usage is correct. One of the command line parameters is the name of a file which contains the configuration of the virtual parallel machine. The syntax of a configuration file is as follows:

my %debug = (
  host1 => 0,
  host2 => 0,
  host3 => 0,
  host4 => 0,
  ...
  IP address/name => 0 | 1,
);

my %max_num_proc = (
  host1 => 1,
  host2 => 2,
  host3 => 1,
  host4 => 3,
  ...
  IP address/name => N,
);

return (\%debug, \%max_num_proc);

The variable %debug allows to activate the GRID::Cluster debug mode in every machine of the virtual parallel machine. On the other hand, the variable %max_num_proc stores the maximum number of processes that can be instantiated in every machine of the virtual parallel machine. These two variables are initialized at line 23.

The variable @machine stores the IP addresses/names of the machines where a user has SSH access. These machines will constitute the virtual parallel machine. At line 25 the machines are sorted taking into account the maximum number of processes supported by each one.

27 my $c = GRID::Cluster->new(host_names => \@machine, debug => $debug, max_num_np => $max_num_np)
28    || die "No machines has been initialized in the cluster";
29
30 $np ||= $c->get_num_machines();
31
32 $c->copyandmake(
33       dir => 'pi',
34       makeargs => 'pi',
35       files => [ qw{pi.c Makefile} ],
36       cleanfiles => $clean,
37       cleandirs => $clean, # remove the whole directory at the end
38       keepdir => 1,
39     );
40
41 $c->chdir("pi/") || die "Can't change to pi/\n";

At line 27 a new GRID::Cluster object is instantiated, using the method new. The number of processes is obtained from an argument specified in the command line by the user, or by the use of the method get_num_machines at line 30. The call to copyandmake at lines 32-39 copies (using scp) the files pi.c and Makefile to a directory named pi on the remote machine. The directory pi will be created if it does not exists. After the file transfer, the command specified by the option make will be executed with the arguments specified in the option makeargs. If the make option isn't specified but there is a file named Makefile between the transferred files, the make program will be executed. Set the make option to number 0 or the string '' to avoid the execution of any command after the transfer. The transferred files will be removed when the connection finishes if the option cleanfiles is set. More radical, the option cleandirs will remove the created directory and all the files below it. Observe that the directory and the files will be kept if they were not created by this connection. The call to copyandmake by default sets dir as the current directory in the remote machine. Set the option keepdir to one to avoid this. The method chdir (line 41) of a GRID::Cluster object changes the working directory of every remote machine associated to the virtual parallel machine.

43 my @commands = map {  "./pi $_ $N $np |" } 0..$np-1;
44
45 my $t0 = [gettimeofday];
46
47 my $pi = sum @{$c->qx(@commands)};
48
49 my $elapsed = tv_interval($t0);
50
51 print "Calculating Pi with $N iterations and $np processes\n";
52 print "Elapsed Time: $elapsed seconds\n";
53 print "Pi Value: $pi\n";

Last step consists in creating the commands that are going to be executed in different machines (line 43) by the use of the method qx of a GRID::Cluster object. This method allows the execution of different tasks or processes following an approximation based on farms, this is, initially, a maximum number of processes are run, and when one of them finishes its execution, a new process is run, if there are more pending processes to be executed. This feature allows a good load balancing among different machines.

At line 47, the method qx returns a list with the partial sums calculated by every process executed in the virtual parallel machine, and by the use of the function sum, a sum of all these results is performed, obtaining the value of the number Pi.

COMPUTATIONAL RESULTS

The execution of the C program on each of the three involved machines is presented in following lines. The number of intervals N has been fixed to 1,000,000,000.

$ time ./pi 0 1000000000 1
3.141593
real    0m56.959s
user    0m56.492s
sys     0m0.004s

$ time ./pi 0 1000000000 1
3.141593
real    0m30.862s
user    0m30.850s
sys     0m0.012s

$ time ./pi 0 1000000000 1
3.141593
real    0m29.026s
user    0m28.654s
sys     0m0.049s

These results indicate that the first machine is slower than the other two.

Now let us run the driver using only the fastest machine and one process. The time spent is comparable to the pure C time, and that is great because the overhead introduced by the coordination tasks is not as large:

$ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 1
Calculating Pi with 1000000000 iterations and 1 processes
Elapsed Time: 30.919523 seconds
Pi Value: 3.141593

real    0m32.690s
user    0m0.516s
sys     0m0.060s

Now we are going to execute the driver using two different machines, each one with only one process:

$ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 2
Calculating Pi with 1000000000 iterations and 2 processes
Elapsed Time: 28.459958 seconds
Pi Value: 3.141592

real    0m30.610s
user    0m0.524s
sys     0m0.056s

We can see that the sequential pure C version took 56 seconds in the slowest machine. By using two machines, each one with one process, the time has been reduced to 23 seconds. This a factor of 56/31 = 1.80 times faster. This factor is even better if I don't consider the set-up time: 56/29 = 1.93. The total time decreases if three machines are used, every one with only one process:

$ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 3
Calculating Pi with 1000000000 iterations and 3 processes
Elapsed Time: 20.956588 seconds
Pi Value: 3.141594

real    0m22.549s
user    0m0.296s
sys     0m0.068s

which gives a speed factor of 56/23 = 2.43 or not considering the set-up time 56/21 = 2.66.

If you increase the number of processes, the use of the method qx allows to obtain better results, due to the load balancing produced by the use of a mechanism based on a farm. The results increasing the number of processes (but only using three machines, every one with a process in every moment) are in the following lines:

$ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 6
Calculating Pi with 1000000000 iterations and 6 processes
Elapsed Time: 15.694753 seconds
Pi Value: 3.141594

real    0m17.285s
user    0m0.304s
sys     0m0.104s

$ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 12
Calculating Pi with 1000000000 iterations and 12 processes
Elapsed Time: 13.246352 seconds
Pi Value: 3.141588

real    0m14.798s
user    0m0.328s
sys     0m0.116s

$ time ./pi_grid.pl -co MachineConfig.pm -N 1000000000 -np 15
Calculating Pi with 1000000000 iterations and 15 processes
Elapsed Time: 12.924256 seconds
Pi Value: 3.1416

real    0m14.500s
user    0m0.372s
sys     0m0.108s

Using 3 processes with 3 machines (every one with only one process), the fastest machines have to wait for the slowest one to finish the execution. Using 6, 12 and 15 processes, the time is decreased. Because of the heterogeneity of the different machines, while the slowest machine is executing a process, the fastest one has executed several processes. More processes are executed in less time by the fastest machine (load balancing) and the consequence is a decrease in the total execution time.

SEE ALSO

  • GRID::Cluster

  • GRID::Cluster::Result

  • GRID::Cluster::Tutorial

  • GRID::Machine

  • IPC::PerlSSH

  • Man pages of ssh, ssh-key-gen, ssh_config, scp, ssh-agent, ssh-add, sshd

  • http://www.openssh.com

  • The Wikipedia entry in Cluster Computing http://en.wikipedia.org/wiki/Computer_cluster

  • The Wikipedia entry in GRID Computing: http://en.wikipedia.org/wiki/Grid_computing

  • The Wikipedia entry for Load Balancing http://en.wikipedia.org/wiki/Load_balancing_%28computing%29

  • The State of Parallel Computing in Perl 2007. Perlmonks node at http://www.perlmonks.org/?node_id=595771

AUTHORS

Eduardo Segredo Gonzalez <esegredo@ull.es> and Casiano Rodriguez Leon <casiano@ull.es>

AKNOWLEDGEMENTS

This work has been supported by the EC (FEDER) and the Spanish Ministry of Science and Innovation inside the 'Plan Nacional de I+D+i' with the contract number TIN2008-06491-C04-02.

Also, it has been supported by the Canary Government project number PI2007/015.

The work of Eduardo Segredo was funded by grant FPU-AP2009-0457.

COPYRIGHT AND LICENSE

Copyright (C) 2010 by Casiano Rodriguez Leon and Eduardo Segredo Gonzalez. All rights reserved.

This library is free software; you can redistribute it and/or modify it under the same terms as Perl itself, either Perl version 5.12.2 or, at your option, any later version of Perl 5 you may have available.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.