Question

Give brute force algorithm for Hitting Set problem Hint: Hitting Set is ℕℙ-complete, so you can define the certificate to be indicator function of the hitting set, and design the verifier algorithm. Once you have verifier algorithm you need an algorithm that generates every possible certificate and for each generated certificate verifies it.

Answer 1

The Hitting Set problem is an NP-complete problem where a brute force algorithm involves generating all possible subsets as potential hitting sets and verifying each until a valid hitting set is identified or all possibilities are exhausted.

Step-by-step explanation:

The Hitting Set problem is a decision problem in computer science that is known to be NP-complete. To create a brute force algorithm for this problem, we need to perform the following steps:

1. Define the verifier algorithm, which takes as input a set, a collection of subsets of a finite set, and an indicator function (the certificate) that marks elements of the so-called hitting set.
2. Check that each subset in the collection has at least one element marked by the indicator function. If any subset has no marked elements, the certificate is invalid.
3. Generate all possible subsets of the finite set (potential hitting sets) and use the verifier algorithm to check each one.
4. If a valid hitting set is found, the algorithm returns it; otherwise, it concludes that no hitting set exists within the given parameters.

Since the Hitting Set problem is NP-complete, the brute force algorithm would require exponential time in the worst case, making it impractical for large instances.