What are hitting sets?
A hitting set for a collection of sets is a set that has a non- empty intersection with each set in the collection; the hitting set problem is to find a hitting set of minimum cardinality.
What is hitting set problem?
In the Hitting set problem, the objective is to cover the left-vertices using a minimum subset of the right vertices. Converting from one problem to the other is therefore achieved by interchanging the two sets of vertices.
Is hitting set NP hard?
Hitting Set is NP-Hard: In order to prove Hitting Set is NP-Hard, we will perform a reduction from which vertex cover problem can be reduced to the Hitting Set problem.
How do you solve vertex cover problems?
Approach 2(Approximate Algorithm for Vertex Cover): Let the set of all edges in the graph be called E. While E is not empty: Pick a random edge from the set E, add its constituent nodes, u and v into the vertex cover set. For all the edges, which have either u or v as their part, remove them from the set E.
What is a set covering constraint in linear programming?
Introduction. The set covering problem is a significant NP-hard problem in combinatorial optimization. Given a collection of elements, the set covering problem aims to find the minimum number of sets that incorporate (cover) all of these elements.
What is meant by NP hard?
A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP- problem (nondeterministic polynomial time) problem. NP-hard therefore means “at least as hard as any NP-problem,” although it might, in fact, be harder.
Is set cover NP-complete?
Theorem: Set Cover is NP-Complete. Proof: First, we argue that Set Cover is in NP, since given a collection of sets C, a certifier can efficiently check that C indeed contains at most k elements, and that the union of all sets listed in C does include all elements from the ground set U.
What is clique in DAA?
A clique is a subgraph of a graph such that all the vertices in this subgraph are connected with each other that is the subgraph is a complete graph.
What is approximation algorithm in DAA?
An Approximate Algorithm is a way of approach NP-COMPLETENESS for the optimization problem. This technique does not guarantee the best solution. The goal of an approximation algorithm is to come as close as possible to the optimum value in a reasonable amount of time which is at the most polynomial time.
What is the hitting set problem?
1 Hitting set algorithms Given a collection of subsets of V, the hitting set problem is to \fnd the smallest subset S which intersects (hits) every set in .
What is the difference between hitting set and set cover?
Hitting set is an equivalent reformulation of Set Cover. Vertex cover is a special case of Hitting Set. Edge cover is a special case of Set Cover. and the sets are induced by the intersection of the universe and geometric shapes (e.g., disks, rectangles).
Is hitting set is NP-hard?
Hitting Set is NP-Hard: In order to prove Hitting Set is NP-Hard, we will perform a reduction from which vertex cover problem can be reduced to the Hitting Set problem. Now, Let X, that is the ground set = vertices of G.
What is the cardinality subset of the hitting set problem?
The task is then to find a minimum cardinality subset of left-vertices which covers all of the right-vertices. In the Hitting set problem, the objective is to cover the left-vertices using a minimum subset of the right vertices.