The authors present parallel solutions to the AMESCS (all maximal equally-spaced collinear subset) and AMRSS (all maximal regularly-spaced subset) problems and show how their solutions to the latter generalize to the AMRSDLS (all maximal regularly-spaced D-dimensional lattice subsets) problem. Their algorithms differ significantly from the optimal sequential algorithms presented in A.B. Kahng and G. Robins (1991), which do not scale well to (massively) parallel machines. The optimality of the authors' Arbitrary CRCW PRAM (parallel random access machine) algorithms is open; however, the algorithms they present are within a logarithmic factor of optimal. Further, the algorithms are optimal for the mesh-connected computer.
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