Abstract: (1) An approximate center-based clustering that utilizes sampling to cluster a set of n points to identify k>0 centers with quality assurance, but without the drawbacks of sample size and running time dependence on n. (2) An approximate conceptual clustering algorithm that utilizes sampling to identify k disjoint conjunctions with novel quality assurance, also without the drawbacks of sample size and running time dependence on n.

Abstract: An aquarium filter is disclosed that provides an overflow window for indicating a blocked filter cartridge. The filter cartridge extends across the full width of the filter box and includes an overflow weir, or lip. The overflow weir forms part of the filter structure and controls the flow of water when the filter cartridge is blocked. Since the filter cartridge extends across the width of the filter box, the size of the filter for a given flow rate is reduced. The filter provides the feature of overflow indication in a more compact and efficient structure than otherwise possible.