Service Grids like the EGEE Grid can not provide the required number of resources for many VOs. Therefore extending the capacity of these VOs with volunteer or institutional desktop Grids would significantly increase the number of accessible computing resources that can particularly advantageously be exploited in case of parameter sweep applications. This objective has been achieved by the EDGeS project that built a production infrastructure enabling the extension of gLite VOs with several volunteer and institutional desktop Grids. The paper describes the technical solution of integrating service Grids and desktop Grids and, the actual EDGeS production infrastructure. The main objectives and current achievements of the follow-up EDGI project have also been described showing how the existing EDGeS infrastructure can be further extended with clouds.
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