In the lattice of subsets of an n-set X , every maximal Sperner family S may be partitioned into disjoint subfamilies A and B, such that the union of the upset of A with the downset of B yields the entire lattice: U(A) [ D(B) = 2 X . The result generalizes to certain posets.

Let P be the point set in two dimensional plane. In this paper, we consider the problem of locating two isothetic unit squares such that together they cover maximum number of points of P . In case of overlapping, the points in their common zone are counted once. To solve the problem, we propose an algorithm that runs in O(n log n) time using O(n log n) space.

This paper addresses a version of the single-facility Maximal Covering Location Problem on network where demand is: (i) distributed along edges and (ii) uncertain with only known interval estimation. To deal this problem, we propose minmax regret model service facility can be located anywhere network. problem is called Minmax Regret (MMR-EMCLP). Furthermore, present two polynomial algorithms fo...