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Simultaneous localization and mapping (SLAM) is required for mobile robots to be able to explore a prior unknown space without a global positioning reference. Multiple robots can achieve exploration tasks more quickly but with added complexity. A useful representation of the map for SLAM purposes is as an occupancy grid map. In the most general case of multiple-robot SLAM, occupancy grid maps from multiple agents must be merged in real time without any prior knowledge of their relative transformation. In addition, the probabilistic information of the maps must be accounted for and fused accordingly. In this article, the generalized Voronoi diagram (GVD) is extended to encapsulate the probabilistic information encoded in the occupancy grid map. The new construct called the probabilistic GVD (PGVD) operates directly on occupancy grid maps and is used to determine the relative transformation between maps and fuse them. This approach has three major benefits over past methods: 1) it is effective at finding relative transformations quickly and reliably, 2) the uncertainty associated with transformations used to fuse the maps is accounted for, and 3) the parts of the maps that are more certain are preferentially used in the merging process because of the probabilistic nature of the PGVD.