Set cover problem

Common card · No. 329185

The set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory. Given a set of elements {1, 2, …, n} (henceforth referred to as the universe, specifying all possible elements under consideration) and a collection, referred to as S, of a given m subsets whose union equals the universe, the set cover problem is to identify a smallest sub-collection of S whose union equals the universe. For example, consider the universe, U = {1, 2, 3, 4, 5} and the collection of sets S = { {1, 2, 3}, {2, 4}, {3, 4}, {4, 5} }. In this example, m is equal to 4, as there are four subsets that comprise this collection. The union of S is equal to U. However, we can cover all elements with only two sets: { {1, 2, 3}, {4, 5} }‍, but not with only one set. Therefore, the solution to the set cover problem for this U and S has size 2. This example is illustrated in the picture above. More formally, given a universe...

Read on Wikipedia · Image Jochen Burghardt, CC BY-SA 4.0