Optical burst switching (OBS) is a promising paradigm for the next-generation Internet. In OBS, a key problem is to schedule bursts on wavelength channels, whose bandwidth may become fragmented with the so-called void (or idle) intervals, using both fast and bandwidth efficient algorithms so as to reduce burst loss. To date, two well-known scheduling algorithms, called Horizon and LAUC-VF, have been proposed in the literature, which trade off bandwidth efficiency for fast running time and vice versa, respectively. In this paper, we propose a set of novel burst scheduling algorithms for OBS networks with and without fiber delay lines (FDLs) utilizing the techniques from computational geometry. In networks without FDLs, our proposed minimum-starting-void (Min-SV) algorithm can schedule a burst in O(logm) time, where m is the total number of void intervals, as long as there is a suitable void interval. Simulation results suggest that our algorithm achieves a loss rate which is at least as low as LAUC-VF, but can run much faster. In fact, its speed can be almost the same as Horizon (which has a much higher loss rate). In networks with FDLs, our proposed batching FDL algorithm considers a batch of FDLs to find a suitable FDL to delay a burst which would otherwise be discarded due to contention, instead of considering the FDLs one by one. The average running time of this algorithm is therefore significantly reduced from that of the existing burst scheduling algorithms. Our algorithms can also be used as algorithmic tools to speed up the scheduling time of many other void-filling scheduling algorithms.