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The evaluation of regular path queries (RPQ), in the sense of returning all endpoint pairs, can be performed in polynomial time.To do this, for every endpoint pair, we can see the graph database as a finite automaton, also represent the regular path query as a finite automaton, and check if a suitable path exists by checking that the intersection of both languages is nonempty (i.e., solving ...
To decide if a graph has a Hamiltonian path, one would have to check each possible path in the input graph G. There are n! different sequences of vertices that might be Hamiltonian paths in a given n-vertex graph (and are, in a complete graph), so a brute force search algorithm that tests all possible sequences would be very slow.
A three-dimensional hypercube graph showing a Hamiltonian path in red, and a longest induced path in bold black. In graph theory, a path in a graph is a finite or infinite sequence of edges which joins a sequence of vertices which, by most definitions, are all distinct (and since the vertices are distinct, so are the edges).
In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle that visits each vertex exactly once. A Hamiltonian path that starts and ends at adjacent vertices can be completed by adding ...
That is, a path exists from the first vertex in the pair to the second, and another path exists from the second vertex to the first. In a directed graph G that may not itself be strongly connected, a pair of vertices u and v are said to be strongly connected to each other if there is a path in each direction between them.
Shortest path (A, C, E, D, F) between vertices A and F in the weighted directed 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.
In case multiple choices for p u exist, choose p u for which there exists a shortest path from v to p u with as few edges as possible; this tie-breaking rule is needed to prevent loops when there exist zero-length cycles. Construct the shortest-path tree using the edges between each node and its parent.
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