INSTALLING MYSQL ON CENTOS WITHOUT ROOT ACCOUNT:

1. Download MySQL Community Server 5.5.8 Linux - Generic Compressed TAR Archive

2. Unpack it. For example to: /home/martin/mysql

3. Create my.cnf file in your home directory. The file contents should be:
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[server]
user=martin
basedir=/home/martin/mysql
datadir=/home/martin/sql_data
socket=/home/martin/socket
port=3666
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4. Go to the /home/martin/mysql directory and execute:
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./scripts/mysql_install_db --defaults-file=~/my.cnf --user=martin --basedir=/home/martin/mysql --datadir=/home/martin/sql_data --socket=/home/martin/socket
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Note that --defaults-file MUST be the first parameter, otherwise it won't work! It's a MySQL bug.

5. Your MySQL server is ready. Start it with this command:
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./bin/mysqld_safe --defaults-file=~/my.cnf &
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6. Connecting to server:
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mysql -h 127.0.0.1 -P 3666 -u root -p (using tcp)
or
mysql --socket=/home/martin/socket -u root -p (using unix socket)
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7. Shutting down server:
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mysqladmin -h 127.0.0.1 -P 3666 -u root shutdown(using tcp)
or
mysqladmin --socket=/home/martin/socket -u root shutdown (using unix socket)
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Source: http://superuser.com/questions/209203/how-can-i-install-mysql-on-centos-without-being-root-su