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What is Kahn's algorithm?

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In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.

What is the longest path in a graph?

A longest path between two given vertices s and t in a weighted graph G is the same thing as a shortest path in a graph −G derived from G by changing every weight to its negation. Therefore, if shortest paths can be found in −G, then longest paths can also be found in G.

How do you find the longest path on a graph in DFS?

We can call the DFS function from every node and traverse for all its children. The recursive formula will be: dp[node] = max(dp[node], 1 + max(dp[child1], dp[child2], dp[child3]..)) At the end check for the maximum value in dp[] array, which will be the longest path in the DAG.Jun 15, 2021

Why is longest path NP?

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 Hamilton path NP hard?

Any Hamiltonian Path can be made into a Hamiltonian Circuit through a polynomial time reduction by simply adding one edge between the first and last point in the path. Therefore we have a reduction, which means that Hamiltonian Paths are in NP Hard, and therefore in NP Complete.Feb 24, 2015

image-What is Kahn's algorithm?
image-What is Kahn's algorithm?
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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).Dec 3, 2019

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Can BFS find longest path?

BFS runs in worst-case time , where is the number of nodes, and is the number of edges in the graph. As such, it can't compute longest paths, since it is NP-hard [1].

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Can Dijkstra's be used to find the longest path in a graph?

The Dijkstra Algorithm is an algorithm that allows you to allocate the shortest path in a graph between a starting node i and an end note j by inlcuding other nodes of the graph. It can also be used to calculate longest paths, if some simple modifications are used.

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Can Bellman Ford find the longest path?

For longest path, you could always do Bellman-Ford on the graph with all edge weights negated. Recall that Bellman-Ford works as long as there are no negative weight cycles, and therefore works with any weights on a DAG. Let n=|V(G)| and m=|E(G)|. Let w(a→b) denote the weight of the edge (a→b).

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What is shortest path in a graph?

In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.

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What is the shortest path in a graph?

  • In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized.

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What is the best shortest path algorithm?

  • Dijkstra's Algorithm. Dijkstra's Algorithm stands out from the rest due to its ability to find the shortest path from one node to every other node within the same graph data ...
  • Bellman-Ford Algorithm.
  • Floyd-Warshall Algorithm.
  • Johnson's Algorithm.
  • Final Note.

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What is the longest math equation ever?

  • The longest human representation of a mathematical equation is 499, achieved by Charotar Education Society (India), in Anand, India, on 28 January 2016. The answer to the equation was 100, with 250 digits and 249 maths symbols.

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What is the Long Path?

  • The Long Path is a 357-mile (575 km) long-distance hiking trail beginning at the George Washington Bridge in Fort Lee, New Jersey and ending at Altamont , New York, in the Albany area.

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What is the longest path problem in graph theory?What is the longest path problem in graph theory?

In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.

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How do you find the longest path on a graph?How do you find the longest path on a graph?

For graphs of bounded clique-width, the longest path can also be solved by a polynomial time dynamic programming algorithm. However, the exponent of the polynomial depends on the clique-width of the graph, so this algorithms is not fixed-parameter tractable.

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How do you find the shortest and longest simple path?How do you find the shortest and longest simple path?

Notice that if -G has no negative cycles, finding the shortest simple path is the same as finding the shortest path which can be solved in polynomial time using above algorithms. Finding the longest simple path in general is NP-Hard. This can easily be shown by reducing from the Hamiltonian Cycle problem.

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Is the longest path problem NP-hard?Is the longest path problem NP-hard?

In fact, the Longest Path problem is NP-Hard for a general graph. However, the longest path problem has a linear time solution for directed acyclic graphs. The idea is similar to linear time solution for shortest path in a directed acyclic graph., we use Topological Sorting.

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