Although the title is similar to this one

Finding minimal or canonical expressions for Boolean truth tables

that topic should be about something else.

Given a vector consisting of "n" slots, the objective is to choose the minimum number of vectors that can "fill" these slots. For example,

For n = 10,

Vec 1: 0 0 1 1 0 0 1 1 0 0

Vec 2: 0 0 0 0 1 0 0 0 0 0

Vec 3: 1 1 0 0 1 1 0 0 1 1

So Vec 1 and Vec 3 will be chosen.

There can exist no solutions to fill all the "n" slots and in that case, we want to fill as many as possible.

The Quine–McCluskey algorithm is also not applicable because the objective function is different.

My computer friend suggests me about "Genetic algorithm" but I wonder whether there exists any deterministic algorithm to solve this problem.