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 ...

In this paper, for the purpose of saving network resources, we first introduce and investigate a new problem referred to as the least hop(s) multiple additively constrained path (LHMACP) selection, which is NP-complete. Then, we propose the k-shortest paths Extended BellmanFord (k-EB) algorithm, which is capable of computing All Hops k-shortest Paths (AHKP) between a source and a destination. T...

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’...

Let S be a subdivision of the plane into polygonal regions, where each region has an associated positive weight. The weighted region shortest path problem is to determine a shortest path in S between two points s, t ∈ R, where the distances are measured according to the weighted Euclidean metric—the length of a path is defined to be the weighted sum of (Euclidean) lengths of the sub-paths withi...

A new algorithm to compute the K shortest paths (in order of increasing length) between a given pair of nodes in a digraph with n nodes and m arcs is presented. The algorithm recursively and efficiently solves a set of equations which generalize the Bellman equations for the (single) shortest path problem and allows a straightforward implementation. After the shortest path from the initial node...

Path in a graph. The shortest path weight for a pair (u, v) of edges is defined as: δ(u, v) = ∞, if there is no path from u to v; δ(u, v) = min(w(p)): p connects u to v. A shortest path between u and v is any path p between them, such that w(p) = δ(u, v). Single-source shortest path problem. Given a graph G and a vertex v ∈ V , find the shortest path from v to every other node in the graph. Sin...

We consider the problem of enumerating, in order of increasing length, the K shortest paths between a given pair of nodes in a weighted digraph G with n nodes and m arcs. To solve this problem, Eppstein’s algorithm first computes the shortest path tree and then builds a graph D(G) representing all possible deviations from the shortest path. Building D(G) takes O(m+n log n) time in the basic ver...

If the given problem instance is partially solved, we want to minimize our effort to solve the problem using that information. In this paper we introduce the measure of entropy, H(S), for uncertainty in partially solved input data S(X) = (X1, ..., Xk), where X is the entire data set, and each Xi is already solved. We propose a generic algorithm that merges Xi’s repeatedly, and finishes when k b...

In this paper, we apply an efficient top-k shortest distance routing algorithm to the link prediction problem and test its efficacy. We compare the results with other base line and state-of-the-art methods as well as with the shortest path. Our results show that using top-k distances as a similarity measure outperforms classical similarity measures such as Jaccard and Adamic/Adar.