In order to achieve the best application-level Quality-of-Service (QoS), complex multimedia applications need to be dynamically tuned and reconfigured to adapt to unpredictable open environments offered by general-purpose systems. We believe that the objective of such adaptations should be to maintain a stable QoS with respect to a set of critical application QoS parameters. However, we have observed that only a limited set of parameters may be used as "tuning knobs" to affect the application behavior. In this paper, we present a hierarchical graph model to discover the relationships between the sets of tunable and critical QoS parameters. Based on such a model, we propose a polynomial complexity QoS probing algorithm to quantitatively capture the run-time relationships between the two sets of parameters. Our probing algorithm is integrated into our broader framework, Agilos, which uses a configurable visual tracking application to verify the effectiveness of adaptations.