We study the problem of constructing graphs from shortest path information (complete or partial). Consider graphs with labeled vertices and edges. Given a collection V of vertices and for each u 2 V a positive integer d(u), and a family F u = fF u;i : i < d(u)g of subsets of V construct a graph such that for each u and each link i of u, F u;i is the set of nodes having an optimal length path to...

In this paper, we study the following all-pair shortest path query problem: Given the interval model of an unweighted interval graph of n vertices, build a data structure such that each query on the shortest path (or its length) between any pair of vertices of the graph can be processed eeciently (both sequentially and in parallel). We show that, after sorting the input intervals by their endpo...

We consider the problem of computing the optimal swap edges of a shortest-path tree. This theoretical problem arises in practice in systems that offer point-offailure shortest-path rerouting service in presence of a single link failure: if the shortest path is not affected by the failed link, then the message will be delivered through that path; otherwise, the system will guarantee that, when t...

The shortest path problem asks for a path between two given points such that the sum of its edges is minimized. The problem has a rich history and has been studied extensively since the 1950’s in many areas of computer science, among them network optimization, graph theory and computational geometry. In this chapter we consider two versions of the problem; the shortest path in a transportation ...

Consider the following modification to the shortest path query problem in polygonal domains: instead of finding shortest path to a query point q, we find the shortest path to any point that sees q. We present an interactive visualization applet visualizing these quickest visibility paths. The applet also visualizes quickest visibility maps, that is the subdivision of the domain into cells by th...

Shortest path problems occupy an important position in Operations Research as well as in Artificial Intelligence. In this paper we study shortest path algorithms that exploit heuristic estimates. The well-known algorithms are put into one framework. Besides we present an interesting application of binary numbers in the shortest path theory.

Shortest Path Problem where the time/cost have vague value is one of the most studied problems in Fuzzy sets and systems area. Thus numerous articles have focused on the Fuzzy Shortest Path Problem (FSPP) in a network. This paper, presents the fuzzy shortest length heuristic procedure if the length of the path in the network is trapezoidal fuzzy set where the highest similarity degree is utiliz...

We study the problem of finding small integer arc lengths in a digraph such that some given paths are uniquely determined shortest paths. This Inverse Shortest Paths (ISP) problem arises in the planning of shortest path networks. We present an O(|V |)-approximation algorithm for ISP and show that minimizing the longest arc or the longest path length is APX -hard. Thus, deciding if a given path ...

We present an obstacle avoiding path planning method based on a Voronoi diagram. We use a tactical visibility measure to obtain the shortest path length with the lowest local probability to be discovered based on the map topology. A Voronoi-based navigation mesh for finding the shortest smooth path with the lowest visibility along the path is used. The piecewise linear rough path in the Voronoi...

k-Interval Routing Scheme (k-IRS) is a compact routing method that allows up to k interval labels to be assigned to an arc; and global k-IRS allows not more than a total of k interval labels in the whole network. A fundamental problem is to characterize the networks that admit k-IRS (or global k-IRS). Many of the problems related to single-shortest-path k-IRS have already been shown to be NP-co...