Is the knapsack problem NP-complete?

Theorem 1 Knapsack is NP-complete. Proof: First of all, Knapsack is NP. The proof is the set S of items that are chosen and the verification process is to compute ∑i∈S si and ∑i∈S vi, which takes polynomial time in the size of input. problem.

How do you prove knapsack is NP-complete?

3-SAT → SUBSET-SUM → KNAPSACK, which completes the proof that KNAPSACK is NP complete.

Is Subset Sum and knapsack problem NP-complete?

Clearly, the Knapsack (Subset Sum) Problem re- duces to the 0 -1 Knapsack Problem, and thus the 0 -1 Knapsack Problem is also NP-complete.

Is knapsack problem solvable?

Knapsack problems are easily solved by dynamic programming.

What is knapsack problem with example?

The 0/1 knapsack problem means that the items are either completely or no items are filled in a knapsack. For example, we have two items having weights 2kg and 3kg, respectively. If we pick the 2kg item then we cannot pick 1kg item from the 2kg item (item is not divisible); we have to pick the 2kg item completely.

Can NP-complete be reduced?

Yes. By definition any NP problem can be reduced to an NP-complete problem in polynomial time. Since NP-complete problems are themselves NP problems, all NP-complete problems can be reduced to each other in polynomial time.

Is shortest path NP-complete?

Since it is also in NP, it is NP-Complete. The shortest path on the other hand is a different one, it asks what is the shortest way from point A to point B, and it is in P because there is a polynomial time algorithm that solves it (Dijkstra’s algorithm, Bellman-Ford, BFS for non weighted graphs).

Is the knapsack problem NP complete or not?

The Knapsack problem is NP, and any problem in NP can be reduced to an NP complete problem (Cook’s Theorem). So to show that the knapsack problem is NP complete it is sufficient to show that an NP-complete problem is reducible to the Knapsack problem.

Why is the reduction from exact cover to knapsack problem polytime?

The reduction is polytime because p (n) steps are needed to “translate” any input of the Exact Cover problem into an input of the Knapsack problem, where p (n) is some polynomial Is it correct?? Could I improve something?? Are the indices that I used correct?? Show activity on this post.

How can the knapsack problem be reduced to a set sum problem?

Therefore, the knapsack problem can be reduced to the Subset-Sum problem in polynomial time. Further, the complexity of this problem depends on the size of the input values,. That is, if there is a way of rounding off the values making them more restricted, then we’d have a polynomial-time algorithm.

Is there a polynomial algorithm for the knapsack problem?

The Knapsack problem as defined in Karp’s paper is NP-Complete since there is a reduction from other NPC problem (Exact Cover, in this case) to Knapsack. This means that there is no polynomial algorithm that can solve all instances of the Knapsack problem, unless P = NP.