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 answer is doing.”
—English proverb, collected in George Herbert, Jacula Prudentum (1651)
“Often on bare rocky carries the trail was so indistinct that I repeatedly lost it, but when I walked behind him I observed that he could keep it almost like a hound, and rarely hesitated, or, if he paused a moment on a bare rock, his eye immediately detected some sign which would have escaped me. Frequently we found no path at all at these places, and were to him unaccountably delayed. He would only say it was “ver strange.””
—Henry David Thoreau (1817–1862)
“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)