Shortest path problems are a well-studied class of problems in theoretical computer science. One particularly applicable type of shortest path problem is to find the geodesic shortest path on a terrain. This type of algorithm finds the shortest path between two points that stays on the surface of a terrain. The most popular methods for finding such a shortest path involve a variant of Dijkstra’...

We study the problem of embedding shortest-path metrics weighted graphs into $\ell_p$ spaces. introduce a new technique based on low-depth decompositions graph via shortest paths. The notion Shortest Path Decomposition depth is inductively defined: A (weighed) path has decomposition (SPD) $1$. General an SPD $k$ if it contains whose deletion leads to graph, each components at most $k-1$. In thi...