Providing QoS guarantees to the applications in a multi-institutional Grid is a challenging task. Although advance reservations (ARs) can provide QoS guarantees for the applications, they often seriously degrade system performance for resource owners. In this paper, we present a framework for AR based resource sharing that not only provides QoS guarantees for the applications but also ensures high utilization of the resources. This paper focuses on the application-to-resource mapping component of the framework as our results show that traditional mapping algorithms used with best effort jobs do not perform well for ARs. The paper proposes a set of algorithms for mapping ARs and investigates their performance in detail. The paper then presents a novel algorithm that outperforms a number of other algorithms in almost every respect for a wide range of workload parameters. Rigorous experimentation proves the efficacy of our algorithm and brings important insights into the dynamics of the system.