 # Is NP Complete The Longest Path?

## How do you know if a problem is NP complete?

To prove something is NP-Complete, there are 2 steps:Prove the problem is in NP, that is, you can verify whether a proposed solution to your problem is an actual solution in polynomial time.Show that every problem in NP reduces to your problem in polynomial time..

## Why is longest path NP complete?

Now it is easy to conclude that Longest Path is NP-complete because it is in NP and HamiltonianPath ∝ LongestP ath simply by observing that there is a Hamiltonian path in G if and only if there is a path of length n − 1.

## 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).

## What does NP hard stand for?

non-deterministic polynomial-time hardnessIn computational complexity theory, NP-hardness (non-deterministic polynomial-time hardness) is the defining property of a class of problems that are informally “at least as hard as the hardest problems in NP”.

## How do you find the shortest path?

Dijkstra’s algorithm can be used to find the shortest path. This algorithm will continue to run until all of the reachable vertices in a graph have been visited, which means that we could run Dijkstra’s algorithm, find the shortest path between any two reachable nodes, and then save the results somewhere.

## What does NP Complete mean?

nondeterministic polynomialA 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 are polynomial-time reducible to it, the problem is NP-complete.

## Is Path NP complete?

3 Answers. The shortest (in terms of weight) path, constrained to have exactly n (or at most n) edges, can be found in polynomial time. … If repetitions are disallowed, and G has n+1 vertices, then the shortest length-n path is just a Traveling salesman path, so of course it’s NP-complete.

## Is P equal to NP?

The Clay Mathematics Institute in Cambridge, MA, has named “P versus NP” as one of its “Millennium” problems, and offers \$1 million to anyone who provides a verified proof. But “P versus NP” is more than just an abstract mathematical puzzle. … Practical experience overwhelmingly suggests that P does not equal NP.

## Who invented Dijkstra algorithm?

Edsger W. DijkstraDijkstra’s algorithm (or Dijkstra’s Shortest Path First algorithm, SPF algorithm) is an algorithm for finding the shortest paths between nodes in a graph, which may represent, for example, road networks. It was conceived by computer scientist Edsger W. Dijkstra in 1956 and published three years later.

## Does A * find the shortest path?

3 Answers. A-star is guaranteed to provide the shortest path according to your metric function (not necessarily ‘as the bird flies’), provided that your heuristic is “admissible”, meaning that it never over-estimates the remaining distance.

## Can a Hamiltonian path repeat edges?

A Hamiltonian path visits every node (or vertex) exactly once, and a Eulerian path traverses every edge exactly once. They are related but are neither dependent nor mutually exclusive. … As a result, vertices can be repeated but edges cannot.

## Is minimum spanning tree NP complete?

The degree constrained minimum spanning tree is a minimum spanning tree in which each vertex is connected to no more than d other vertices, for some given number d. The case d = 2 is a special case of the traveling salesman problem, so the degree constrained minimum spanning tree is NP-hard in general.

## Is traveling salesman NP complete?

The simple answer is that it’s NP-hard, but it’s not in NP. Since it’s not in NP, it can’t be NP-complete. In TSP you’re looking for the shortest loop that goes through every city in a given set of cities. … Since it takes exponential time to solve NP, the solution cannot be checked in polynomial time.

## Can Dijkstra find longest path?

Dijkstra cannot be used to compute the longest path. Or if it can, it wouldn’t be efficient. Simply do the edge relax to all edges in topological order. It will be the most efficient method.

## Is Hamiltonian path NP complete?

The problem is to determine if there is a simple path that crosses each vertex of the graph. A Hamiltonian path is a simple open path that contains each vertex in a graph exactly once. … Hamiltonian Cycle is NP-complete, so we may try to reduce this problem to Hamiltonian Path.

## Is Dijkstra algorithm optimal?

Dijkstra’s algorithm is used for graph searches. It is optimal, meaning it will find the single shortest path. It is uninformed, meaning it does not need to know the target node before hand. In fact it finds the shortest path from every node to the node of origin.

## What are the shortest path algorithms?

Given a graph and a source vertex in the graph, find shortest paths from source to all vertices in the given graph. Dijkstra’s algorithm is very similar to Prim’s algorithm for minimum spanning tree.

## What is the best shortest path algorithm?

Dijkstra finds the shortest path from only one vertex, Floyd-Warshall finds it between all of them. Use the Floyd-Warshall algorithm if you want to find the shortest path between all pairs of vertexes, as it has a (far) higher running time than Dijkstra’s algorithm.