I would appreciate if somebody could recommend a good Swiss pairing program. I'd prefer online version with multi-language option and free version but cheap one is also good.
I've found http://www.free-swiss.com/ but do you know other ones?
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My club uses Swiss Manager. It is very good but not cheap. 150 euros for the full version, 75 euros for the light. It is perhaps worth looking at what it does to get ideas if you are thinking of writing your own.
One I downloaded some time ago but still haven't got round to playing (so I can't give any recommendation) is OSwiss which is a project on Sourceforge.
You could try this free service: https://swisssystem.org/
It’s simple and easy to use. It works fine on mobile devices. The maximum player count is 200.
SWIPS is also online tool for managing tournaments. It includes much more than just a swiss system and round robin, but you can use it solely for that purpose if you want.
Right now its free, available languages are English and Slovak.
An offline alternative is Vegachess, which it is also homologated by FIDE. AFAIK Vegachess just uses javafo as its pairing engine. Linux version of vegachess is free to use and Windows version not very expensive.
E2-E4 online pairing program is now available for everyone. Previously it was used organizers for pairing and to show results in a real time in Russia - chessresults.ru project.
This program can be used on any kind of devices, but especially it designed for mobile devices. Arbiters/trainers with tablets can manage chess tournament much more effectively and faster.
There are three pairing systems: Swiss (based on JaVaFo), Round-robin and Manual. To figure out all features, its better to see documentation which isn't ready yet, but this lack will disappear soon. And if someone wants to translate program to your own language, so you are welcome :)
If you are looking for an easy-to-use, FIDE-approved online platform, take a look at ChessManager.