How about Single-Linkage Clustering or Complete-Linkage Clustering, both belong to hierarchical Clustering, you just have to choose a distance metric that works on the grid, like Manhattan Distance.
Actually shouldn't it be possible to adopt any Clustering algorithm: as an example k-means: you need to choose an appropriate distance metric as above and second adjust the calculation of the prototypes to choose a point of the grid.
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How about Single-Linkage Clustering or Complete-Linkage Clustering, both belong to hierarchical Clustering, you just have to choose a distance metric that works on the grid, like Manhattan Distance.
Actually shouldn't it be possible to adopt any Clustering algorithm: as an example k-means: you need to choose an appropriate distance metric as above and second adjust the calculation of the prototypes to choose a point of the grid.