Optical burst switching (OBS) is an emerging technology that allows variable size data bursts to be transported directly over dense wavelength division multiplexing links. In order to make OBS a viable solution, the burst-scheduling algorithms need to be able to utilize the available wavelengths efficiently, while being able to operate fast enough to keep up with the burst incoming rate. For example, for a 16-port OBS router with 64 wavelengths per link, each operating at 10 Gb/s, we need to process one burst request every 78 ns in order to support an average burst length of 100 kB. When implemented in hardware, the well-known horizon scheduler has O(1) runtime for a practical number of wavelengths. Unfortunately, horizon scheduling cannot utilize the voids created by previously scheduled bursts, resulting in low bandwidth utilization. To date, minimum starting void is the fastest scheduling algorithm that can schedule wavelengths efficiently. However, while its complexity is O(log m), it requires 10 log m memory accesses to schedule a single burst. This means that it can take up to several microseconds for each burst request, which is still too slow to make it a practical solution for OBS deployment. In this paper, we propose an optimal burst scheduler using constant time burst resequencing (CTBR), which has O(1) runtime. The proposed CTBR scheduler is able to produce optimal burst schedules while having processing speed comparable to the horizon scheduler. The algorithm is well suited to high- performance hardware implementation.