Set Partition , approximation, optimal solution --need help in designing algorithm and writing its psedocode in latex

Question

Let S = {S1, . . . , Sn} be a set of sets of integers, e.g. S = {{1, 3}, {2, 4}, {3, 4}, {2, 5}}. We say that D = {D1, . . . , Dk} is a partition of S if the following conditions hold. • Di ⊆ S for every i ∈ {1, . . . , k} • All sets in D are pairwise disjoint. • D1 ∪ D2 ∪ · · · ∪ Dk = S The problem consists in finding a partition D of S such that: • The cardinality of D is a minimum • For every Di ∈ D it holds that ∩S∈DiS != ∅. Your task is need your help to Design an algorithm that gives a solution or an approximated solution and also pseudocode description of the algorithm in latex. explain the rationality behind your algorithm.