The Moving Object Processing System (MOPS) team of the University of Hawaii's Pan-STARRS telescope is developing software to automatically discover and identify > 90% of near-Earth objects (NEOs) larger than 300 m, and > 80% of other classes of asteroids and comets. MOPS relies on new, efficient, multiple-hypothesis KD-tree and variable-tree search algorithms to search the similar to 10(12) detection pairs that are expected per night. Candidate intra- and inter-night associations of detections are evaluated for consistency with a real solar system object, and orbits are computed. We describe the basic operation of the MOPS pipeline, identify pipeline processing steps that are candidates for multiple-hypothesis spatial searches, describe our implementation of those algorithms, and provide preliminary results for MOPS.