A multi-clip query requests multiple video clips be returned as the answer of the query. In 
many applications and situations, the order in which these clips are to be delivered does 
not matter that much to the user. This allows the system ample opportunities to optimize 
system throughput by using schedules that maximize the effect of piggybacking. In this paper, 
we study how to find such optimal schedules. In particular, we consider two optimization 
criteria: (i) one based on maximizing the number of piggybacked clips, and (ii) the other 
based on maximizing the impact on buffer space. We show that the optimal schedule under the 
first criterion is equivalent to a maximum matching in a suitably defined bipartite graph, 
and that under the second criterion, the optimal schedule is equivalent to a maximum 
matching in a suitably defined weighted bipartite graph. Our experimental results, which 
are based on realistic distributions, indicate that both kinds of optimal schedules can 
lead to a gain in throughput of over 300%. And yet the time taken to compute such an 
optimal schedule is only around 1 millisecond.