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.
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) may be modeled by a special case of the shortest path problem in graphs.
Definition
The shortest path problem can be defined for graphs whether undirected, directed, or mixed.
It is defined here for undirected graphs; for directed graphs the definition of path
requires that consecutive vertices be connected by an appropriate directed edge.
Two vertices are adjacent when they are both incident to a common edge.
A path in an undirected graph is a sequence of vertices
such that is adjacent to for .
Such a path is called a path of length
from to .
(The are variables; their numbering here relates to their position in the sequence and needs not to relate to any canonical labeling of the vertices.)
What should a track athlete do when an opponent impedes their path? ... Local coaches weighed in. Who’s to blame? ... At this distance, athletes typically migrate to the inner lane after completion of their staggered start to seize the track’s shortest path.
... of weakness and humiliation.” “The shortest path to regional stability is forcing the Israeli enemy to abide by the (ceasefire) terms it signed,” he said.
19 ... “The shortest path to regional stability is forcing the Israeli enemy to abide by the (ceasefire) terms it signed,” he said ... He added that Palestinian factions have honored their commitments under the ceasefire deal since Jan ... .
Similar to Hezekiah's plight, South African boxers have often had to carve their own paths through adversities. Many, like Matlala, who made history as the world’s shortest professional boxer, defied expectations with sheer determination ... .
Trump threatens to kill Palestinians in Gaza, Hamas if Israeli captives aren’t released ... He also stressed that the shortest path to stability and peace in this region is to "restrain the Zionist regime" and force it to honor its signed commitments.
He accused Israel of reneging on the agreement in an attempt to gain U.S. support to return to aggression ... “And the plot of those is doomed.” ... He added, “The shortest path is to force the enemy to abide by what it has signed.
. Anyone wanting to take the pulse of progressive America can consult the opinion pages of the New York Times... This is the shortest available path out of the political wilderness, if only Democrats find the sense to take it. .