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Yes, there is a proof that the Longest Path Problem is NP-complete.

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3mo ago

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Is finding the longest path in a graph an NP-complete problem?

Yes, finding the longest path in a graph is an NP-complete problem.


What is the longest marked foot path in the US?

The Appalachian Trail is the longest marked foot path in the US.


Is the critical path always the longest path?

The critical path is the sequence of activities that takes all dependencies into account. Thus, it determines the duration of the project, and is necessarily the longest path.


What is the algorithm to find the longest increasing path in a matrix?

The algorithm to find the longest increasing path in a matrix is called the Longest Increasing Path in a Matrix (LIP) algorithm. It involves using dynamic programming to recursively search for the longest increasing path starting from each cell in the matrix. The algorithm keeps track of the length of the longest increasing path found so far and updates it as it explores different paths.


Why is critical path the longest path?

As per the Project Management Terminology, the longest path in a project sequence of activities is called the Critical Path. Because it is the longest path, it determines the duration of the project and hence the finish date of the project given the start date. Since this path is going to determine the schedule/delivery date of the project, it is called the critical path.


What is the longest simple path that can be found in a given graph?

The longest simple path in a graph is the path that does not repeat any vertices and has the most number of edges between two distinct vertices.


What is the longest path in a Directed Acyclic Graph (DAG)?

In a Directed Acyclic Graph (DAG), the longest path is the path with the greatest number of edges between two vertices, without forming a cycle.


Critical path of a project?

The critical path is the longest path (sequence of activities) in a project schedule network diagram. Because it is the longest path, it determines the duration of the project and hence the finish date of the project given the start date


What is the longest path in a tree and how is it determined?

The longest path in a tree is called the diameter. It is determined by finding the two farthest nodes in the tree and calculating the distance between them.


What is the longest increasing path in a matrix and how can it be determined?

The longest increasing path in a matrix is the longest sequence of adjacent cells where each cell's value is greater than the previous cell's value. This can be determined using dynamic programming by recursively exploring all possible paths and keeping track of the length of the longest increasing path encountered.


Which is the longest railway path in the world?

Moscow to Beijing


What is the longest path in a directed acyclic graph?

The longest path in a directed acyclic graph is the path with the greatest total weight or distance between two vertices, without repeating any vertices or going in a cycle.