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...

In this paper, we reduce the logspace shortest path problem to biconnected graphs; in particular, we present a logspace shortest path algorithm for general graphs which uses a logspace shortest path oracle for biconnected graphs. We also present a linear time logspace shortest path algorithm for graphs with bounded vertex degree and biconnected component size, which does not rely on an oracle. ...

In this paper, we reduce the logspace shortest path problem to biconnected graphs; in particular, we present a logspace shortest path algorithm for general graphs which uses a logspace shortest path oracle for biconnected graphs. We also present a linear time logspace shortest path algorithm for graphs with bounded vertex degree and biconnected component size, which does not rely on an oracle. ...

In this article, we study the problem of finding the next-to-shortest path in circular-arc graph. A next-to-shortest path between any pair of vertices in a shortest path amongst all paths between those vertices with length strictly greater than the length of the shortest path. The next-to-shortest path problem in a directed graph in NP-hard. Here we deigned a polynomial time algorithm to solve ...

A shortest-path algorithm finds a path containing the minimal cost between two vertices in a graph. A plethora of shortest-path algorithms is studied in the literature that span across multiple disciplines. This paper presents a survey of shortest-path algorithms based on a taxonomy that is introduced in the paper. One dimension of this taxonomy is the various flavors of the shortest-path probl...

This paper develops a method for solving the single product multi-period production-planning problem, in which the production and the inventory costs of each period arc concave and backlogging is not permitted. It is also assumed that the unit variable cost of the production evolves according to a continuous time Markov process. We prove that this production-planning problem can be Stated as a ...

The shortest path problem is solved and applied to the calculations of half lives with respect to spontaneous fission of heavy nuclei. The dynamical programming method of Bellman and Kalaba is used to find the fission path in the d-dimensional space of deformation parameters. Fission half lives of heavy isotopes (100<Z<110) are shown and compared to the experimental data. 1. Introductory remark...