What is the single source shortest path problem?
The Single-Source Shortest Path (SSSP) problem consists of finding the shortest paths between a given vertex v and all other vertices in the graph. Algorithms such as Breadth-First-Search (BFS) for unweighted graphs or Dijkstra [1] solve this problem.
Is Dijkstra shortest path unique?
The regular Dijkstra “parent” flag is kept as it is. At the end of the algorithm, we run through all nodes of the shortest path (including s and t), and check their “multiple paths” flag. If none are found, the path is unique.
Which is a special case of the shortest path problem?
The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs, where the vertices correspond to intersections and the edges correspond to road segments, each weighted by the length of the segment.
Which is the best algorithm for finding the shortest path?
The distance between vertices v and w, denoted by dist(v,w), is the length of the shortest path between them. The query phase of the shortest path algorithm takes as input a source s and a target t, and returns dist(s,t). Dijkstra’s algorithm [14, 8] is the best-known method for computing shortest paths in our setting.
Which is the label of the shortest path?
r(t) contains a vertex u on a shortest path from s to t. To emphasize that a labeling has the cover property, we call a labeling valid. The query stage of the labeling algorithm is quite simple, given the cover property. Given s and t, find the vertex u ∈ L f(s) ∩ L r(t) that minimizes dist(s,u) + dist(u,t) and return the corresponding path.
Is there a natural solution to the shortest path problem?
A possible solution to this problem is to use a variant of the VCG mechanism, which gives the computers an incentive to reveal their true weights. There is a natural linear programming formulation for the shortest path problem, given below.