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In this article, the authors define this new field. First, they review the \"Grid problem,\" which is defined as flexible, secure, coordinated resource sharing among dynamic collections of individuals, institutions, and resources—what is referred to as virtual organizations. In such settings, unique authentication, authorization, resource access, resource discovery, and other challenges are encountered. It is this class of problem that is addressed by Grid technologies. Next, the authors present an extensible and open Grid architecture, in which protocols, services, application programming interfaces, and software development kits are categorized according to their roles in enabling resource sharing. The authors describe requirements that they believe any such mechanisms must satisfy and discuss the importance of defining a compact set of intergrid protocols to enable interoperability among different Grid systems. 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Yet few tools exist that allow these resources to be exploited effectively in an aggregated form. We present the Condor-G system, which leverages software from Globus and Condor to enable users to harness multi-domain resources as if they all belong to one personal domain. We describe the structure of Condor-G and how it handles job management, resource selection, security, and fault tolerance. We also present results from application experiments with the Condor-G system. 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