The success of prostate brachytherapy critically depends on delivering adequate dose to the prostate gland. Intraoperative localization of the implanted seeds provides potential for dose evaluation and optimization during therapy. A reduced-dimensionality matching algorithm for prostate brachytherapy seed reconstruction (REDMAPS) that uses multiple X-ray fluoroscopy images obtained from different poses is proposed. The seed reconstruction problem is formulated as a combinatorial optimization problem, and REDMAPS finds a solution in a clinically acceptable amount of time using dimensionality reduction to create a smaller space of possible solutions. Dimensionality reduction is possible since the optimal solution has approximately zero cost when the poses of the acquired images are known to be within a small error. REDMAPS is also formulated to address the "hidden seed problem" in which seeds overlap on one or more observed images. REDMAPS uses a pruning algorithm to avoid unnecessary computation of cost metrics and the reduced problem is solved using linear programming. REDMAPS was first evaluated and its parameters tuned using simulations. It was then validated using five phantom and 21 patient datasets. REDMAPS was successful in reconstructing the seeds with an overall seed matching rate above 99% and a reconstruction error below 1 mm in less than 5 s.