Efficient algorithm for finding all maximal subsets

Question

I have a collection of unique sets (represented as bit masks) and would like to eliminate all elements that are proper subsets of another element. For example:

Answer 1

This problem has been studied in literature. Given S_1,...,S_k which are subsets of {1,...,n}, Yellin [1] gave an algorithm to find the maximal subset of {S_1,...,S_k} in time O(kdm) where d is the average size of the S_i, and m is the cardinality of the the maximal subset of {S_1,...,S_k}. This was later improved for some range of parameters by Yellin and Jutla [2] to O((kd)^2/sqrt(log(kd))). It is believed that a truly sub-quadratic algorithm to this problem does not exist.

[1] Daniel M. Yellin: Algorithms for Subset Testing and Finding Maximal Sets. SODA 1992: 386-392.

[2] Daniel M. Yellin, Charanjit S. Jutla: Finding Extremal Sets in Less than Quadratic Time. Inf. Process. Lett. 48(1): 29-34 (1993).