The minimum fractional set cover problem

You hedge your marriage partner in computer science. You can use dating apps in your smart phones recently, so AI may decide your marriage life soon.

m is the cost vector which is yes or no.

F={S1,S2,・・・,Sm}

This is the Linear probing , so you concentrate on your favorite partner.

p is the hedge which is the vector.

p(S) is the total weight of elements in S.

This is the covering problems, so you search for the optimization by expanding.

L is the maximization of p(S).

(1-ε) is approximation algorithm for maximization.

This is feasible, so there is the possibility for your marriage life.