A problem is said to be NP-hard
if everything in NP can be transformed in polynomial time into it even though it may not be in NP
. Conversely, a problem is NP-complete if it is both in NP and NP-hard. … If some NP-complete problem has a polynomial time algorithm, all problems in NP do.
How do I know if I have NP-hard problems?
A problem is said to be NP-hard
if everything in NP can be transformed in polynomial time into it even
though it may not be in NP. Conversely, a problem is NP-complete if it is both in NP and NP-hard.
What does it mean if a problem is 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.
What is NP-hard problem with example?
Examples. An example of an NP-hard problem is the
decision subset sum problem
: given a set of integers, does any non-empty subset of them add up to zero? That is a decision problem and happens to be NP-complete.
Which of the following problems is not NP-hard?
Which of the following problems is not NP complete? Explanation:
Hamiltonian circuit, bin packing, partition problems
are NP complete problems. Halting problem is an undecidable problem.
Is Floyd warshall NP-hard problem?
It is not NP-complete
, because it is not a decision problem. In weighted complete graphs with non-negative edge weights, the weighted longest path problem is the same as the Travelling salesman path problem, because the longest path always includes all vertices.
Are NP-hard problems solvable?
This is known as Cook’s theorem. What makes NP-complete problems important is that if a deterministic polynomial time algorithm can be found to solve one of them,
every NP problem
What makes a problem NP-complete?
A problem is called NP (nondeterministic polynomial) if its solution can be guessed and verified in polynomial time; nondeterministic means that no particular rule is followed to make the guess. If a problem is NP and
all other NP problems
Is it possible for a problem to be in both P and NP?
Is it possible for a problem to be in both P and NP?
Yes
. Since P is a subset of NP, every problem in P is in both P and NP.
How many steps are required to prove that decision problem is NP complete?
| Q. How many steps are required to prove that a decision problem is NP complete? | C. 3 | D. 4 | Answer» b. 2 | Explanation: first, the problem should be np. next, it should be proved that every problem in np is reducible to the problem in question in polynomial time. |
|---|
Is Hamiltonian path NP complete?
The number of calls to the Hamiltonian path algorithm is equal to the number of edges in the original graph with the second reduction. Hence the NP-complete problem Hamiltonian cycle can be reduced to Hamiltonian path, so
Hamiltonian path is itself NP-complete
.
What is Dijkstra shortest path algorithm?
Dijkstra’s algorithm is the iterative algorithmic process to provide us with the
shortest path from one specific starting node to all other nodes of a graph
. It is different from the minimum spanning tree
What is the time complexity of Floyd-Warshall algorithm?
The Floyd-Warshall algorithm is a graph-analysis algorithm that calculates shortest paths between all pairs of nodes in a graph. It is a dynamic programming algorithm with
O(|V|
3
) time
complexity and O(|V|
2
) space complexity.
Can P be reduced to NP?
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 traveling salesman NP-hard?
In Chapter 15 we introduced the Traveling Salesman Problem (TSP) and showed that it is NP-hard (Theorem 15.42). The TSP is perhaps the best-studied NP-hard combinatorial optimization problem, and there are many techniques which have been applied.
