Is set cover problem NP-hard?

Is set cover problem NP-hard?

The set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory. It is one of Karp’s 21 NP-complete problems shown to be NP-complete in 1972. The decision version of set covering is NP-complete, and the optimization/search version of set cover is NP-hard.

Is set cover in P?

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 the time complexity of set cover?

Set Cover is NP-Hard: There is a polynomial time Greedy approximate algorithm, the greedy algorithm provides a Logn approximate algorithm.

Why Is set cover NP-Complete?

Set Cover is in NP: If any problem is in NP, then given a ‘certificate’, which is a solution to the problem and an instance of the problem ( a collection of subsets, C of size k), we will be able to identify (whether solution is correct or not) certificate in polynomial time. Hence, Set Cover is in NP.

Is clique and set cover problem NP-complete?

Since VERTEX-COVER can be reduced to CLIQUE in polynomial time, CLIQUE ∈ NP and VERTEX-COVER is NP-Complete, CLIQUE is also NP-Complete.

What is NP A in sets?

NP is set of decision problems that can be solved by a Non-deterministic Turing Machine in Polynomial time. P is subset of NP (any problem that can be solved by deterministic machine in polynomial time can also be solved by non-deterministic machine in polynomial time).

What set cover?

Buildings insurance – Replacement of sets cover is only available with Home Insurance Ultimate. Where there is a valid claim, this covers the changing or replacement of any associated undamaged items that form part of a matching set or suite that is lost or damaged where a reasonable match cannot be obtained.

What is clique in algorithm?

By convention, in algorithm analysis, the number of vertices in the graph is denoted by n and the number of edges is denoted by m. A clique in a graph G is a complete subgraph of G. That is, it is a subset K of the vertices such that every two vertices in K are the two endpoints of an edge in G.

What is hitting set?

Let be a collection of subsets of a finite set . The smallest subset of that meets every member of. is called the hitting set or Vertex Cover.

Can P be reduced to NP-complete?

Quick reply: No, it does not. Recall the definition of NP-hard problems. A problem X is NP-Hard if every problem in NP can be polynomially reduced to X. If on the other hand a problem X can be polynomially reduced to some NP-complete problem Y, it means that Y is at least as hard as X, not the other way around.

Is 3 SAT problem NP-complete?

Theorem : 3SAT is NP-complete. Proof : Evidently 3SAT is in NP, since SAT is in NP. To determine whether a boolean expression E in CNF is satisfiable, nondeterministically guess values for all the variables and then evaluate the expression. Thus 3SAT is in NP.

Is dominating set same as vertex cover?

The vertex cover ‘covers’ all the edges, but the degree zero vertex is not adjacent to the vertex cover. A dominating set may not be a vertex cover if there is an edge, say e = (u,v), where u and v are both outside the dominating set.

Which is heuristic generates a feasible solution to the set covering problem?

The construction heuristic generates a feasible solution by adding basic elements step by step.

Is the set covering problem a combinatorial problem?

The set covering problem (SCP) is a fundamental combinatorial problem in Operations Research. It is usually described as the problem of covering the rows of this m-row, n-column, zero-one matrix (a ij) by a subset of the columns at minimal cost.

Which is the best heuristic for the unicost problem?

Beasley, 1990, Beasley and Chu, 1996 pointed out that their algorithms based on the Lagrangian relaxation and genetic algorithm were not recommended for unicost problems, since the cost information plays an important role in these algorithms. Jacobs and Brusco (1995) assumed the same point of view for their heuristic based on Simulated Annealing.

Which is the best heuristic for solving SCP?

Since exact methods require substantial computational effort to solve large-scale SCP instances, heuristic algorithms are often used to find a good or near-optimal solution in a reasonable time. Greedy algorithms may be the most natural heuristic approach for quickly solving large combinatorial problems.