You can change a lot of variables in the mysql settings file. This file is called "my.cnf" on linux and "my.ini" on windows. Usually the file is located in /etc/ or /etc/mysql (on linux) and in the mysql program directory on windows.
There are many settings you can change, but what to change them to depends on the server you are running, it's RAM, system load etc.
Make sure to read the mysql manual concerning this topic before changing any settings.
The settings that have the greatest impact seem to be the following:
If you have a lot of profiles in your Logaholic installation, increasing the table_cache variable can help.
Logaholic does a lot of queries that require sorting and limiting, increasing the values for sort_buffer and read_rnd_buffer_size can make this go faster.
Importing logs into Logaholic may go faster by increasing the value for bulk_insert_buffer_size. But, in this case you will also want to give your PHP more memory.
For more information, check out these pages:
Another tool you can use to optimize your mysql settings is the mysqltuner perl script, found here: https://github.com/rackerhacker/MySQLTuner-perl
Finally, the folks a Percona have developed an online mysql configuration wizard that you might like: http://tools.percona.com/