Shortest path problem is a classical and the most widely studied phenomenon in combinatorial optimization. In a classical shortest path problem, the distance of the arcs between different nodes of a network are assumed to be certain. In some uncertain situations, the distance will be calculated as a fuzzy number depending on the number of parameters considered. This article proposes a new appro...

Roads play a vital role to the people live in different places and, from day to day, they travel to schools, to work, to shops, and to transport their goods. Even in this modern world, roads remain one of the mediums used most frequently for travel and transportation. The computation of a shortest path between different locations appears to be a key problem in the road networks. The wide range ...

We numerically show that the statistical properties of the shortest path on critical percolation clusters are consistent with the ones predicted for Schramm-Loewner evolution (SLE) curves for κ = 1.04 ± 0.02. The shortest path results from a global optimization process. To identify it, one needs to explore an entire area. Establishing a relation with SLE permits to generate curves statistically...

There are several applications in VLSI technology that require high-speed shortest-path computations. The shortest path is a path between two nodes (or points) in a graph such that the sum of the weights of its constituent edges is minimum. Floyd-Warshall algorithm provides fastest computation of shortest path between all pair of nodes present in the graph. With rapid advances in VLSI technolog...

Suppose one has a line arrangement and one wants to find a shortest path from one point lying on a line of the arrangement to another such point. We look at a special case: the arrangement consists of two intersecting pencils (sets of lines where all intersect in a point), and the path endpoints are at opposite corners of the largest quadrilateral formed. The open problem was to find a shortest...

The inverse shortest path problem is to minimize the modification on the edge weights such that a predetermined path becomes the shortest one from the origin to the destination with respect to the new edge weights. In this paper, the inverse shortest path problem is considered on a graph with uncertain edge weights. It is shown that the model of the uncertain inverse shortest path problem can b...

We solve a shortest path problem that is motivated by recent interest in pricing networks or other computational resources. Informally, how much is an edge in a network worth to a user who wants to send data between two nodes along a shortest path? If the network is a decentralized entity, such as the Internet, in which multiple self-interested agents own different parts of the network, then au...

Globally shortest path problems have increasing demand due to voluminous datasets in applications like roadmaps, web search engines, mobile data sets, etc., Computing shortest path between nodes in a given directed graph is a very common problem. Among the various shortest path algorithms, Dijkstra’s shortest path algorithm [1] is said to have better performance with regard to run time than the...