We study the efficient evaluation of top-k queries over data items, where the score of each item is dynamically computed by applying an item-specific function whose parameter value is specified in the query. For example, online retail stores rank items by price, which may be a function of the quantity being queried: "Stay 3 nights, get a 15% discount on double-bed rooms." Similarly, while ranking possible routes in online maps by predicted congestion level, the score (congestion) is a function of the time being queried, e.g., "At 5PM on a Friday in Palo Alto, the congestion level on 101 North is high." Since the parameter--the number of nights or the time the online map is queried, in the above examples--is only known at query time, and online applications have stringent response-time requirements, it is infeasible to evaluate every item-specific function to determine the item scores, especially when the number of items is large. Further, space considerations make ...