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.
This is analogous to the problem of finding the shortest path between two intersections on a road map: the graph's vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of its road segment.
Read more about Shortest Path Problem: Definition, Algorithms, Roadnetworks, Applications, Related Problems, Linear Programming Formulation
Famous quotes containing the words shortest, path and/or problem:
“The shortest route is not the most direct one, but rather the one where the most favorable winds swell our sails:Mthat is the lesson that seafarers teach. Not to abide by this lesson is to be obstinate: here, firmness of character is tainted with stupidity.”
—Friedrich Nietzsche (1844–1900)
“The path was a vague parting in the grass
That led us to a weathered windowsill.
We pressed our faces to the pane. “You see,” he said,
“Everything’s as she left it when she died....””
—Robert Frost (1874–1963)
“Give a scientist a problem and he will probably provide a solution; historians and sociologists, by contrast, can offer only opinions. Ask a dozen chemists the composition of an organic compound such as methane, and within a short time all twelve will have come up with the same solution of CH4. Ask, however, a dozen economists or sociologists to provide policies to reduce unemployment or the level of crime and twelve widely differing opinions are likely to be offered.”
—Derek Gjertsen, British scientist, author. Science and Philosophy: Past and Present, ch. 3, Penguin (1989)