The vast adoption of mobile devices with cameras has greatly assisted in the proliferation of the creation and distribution of videos. For a variety of purposes, valuable information may be extracted from these videos. While the computational capability of mobile devices has greatly improved recently, video processing is still a demanding task for mobile devices. Given a network consisting of mobile devices and video-clouds, mobile devices may be able to upload videos to video-clouds, which are more computationally capable for these processing tasks. However, due to networking constraints, when a video processing task is initiated through a query, most videos will not likely have been uploaded to the video-clouds, especially when the query is about a recent event. We investigate the problem of minimal query response time for processing videos stored across a network; however, this problem is a strongly NP-hard problem. To deal with this, we first propose a greedy algorithm with bounded performance. To further deal with the dynamics of the transmission rate between mobile devices and video-clouds, we propose an adaptive algorithm. To evaluate these algorithms, we built an on-demand video processing system. Based on the measurements of the system, we perform simulations to extensively evaluate the proposed algorithms. We also perform experiments on a small testbed to examine the realized system performance. Results show the performance of the greedy algorithm is close to the optimal and much better than other approaches, and the adaptive algorithm performs better with more dynamic transmission rates.