k-Interval Routing Scheme (k-IRS) is a compact routing method that allows up to k interval labels to be assigned to an arc. A fundamental problem is to characterize the networks that admit k-IRS. All of the problems related to single-shortest-path k-IRS have already been shown to be NP-complete. For all-shortest-path k-IRS, the characterization problems have been proved to be NP-complete for ev...

in this paper, shortest path design problem (spdp) in which the path is incident to all cells is considered. the bi-directional path is one of the known types of configuration of networks for automated guided vehi-cles (agv).to solve this problem, two algorithms are developed. for each algorithm an integer linear pro-gramming (ilp) is determined. the objective functions of both algorithms are t...

We propose a dynamic program to find the shortest path in a network having gamma probability distributions as arc lengths. Two operators of sum and comparison need to be adapted for the proposed dynamic program. Convolution approach is used to sum two gamma probability distributions being employed in the dynamic program.

This paper is focussed on algorithms to solve the k-shortest path problem. Three codes were described and compared on rand and grid networks using random generators available on http://www.dis.uniroma1.it/∼challenge9 Codes were also tested on the USA road networks available on the same URL address. One million paths were ranked in less than 3 seconds on random instances with 10 000 nodes and 10...

We study the problem of finding shortest paths in the plane among h convex obstacles, where the path is allowed to pass through (violate) up to k obstacles, for k ≤ h. Equivalently, the problem is to find shortest paths that become obstacle-free if k obstacles are removed from the input. Given a fixed source point s, we show how to construct a map, called a shortest k-path map, so that all dest...

A shortest path problem is a practical issue in networks for real-world situations. This paper addresses the fuzzy shortest path (FSP) problem to obtain the best fuzzy path among fuzzy paths sets. For this purpose, a new efficient algorithm is introduced based on a new definition of ideal fuzzy sets (IFSs) in order to determine the fuzzy shortest path. Moreover, this algorithm is developed for ...

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...

This study considers the addition of relation to an organization structure such that the communication of information between every member in the organization becomes the most efficient. This paper proposes a model of adding relation to a linking pin organization structure where every pair of siblings in a complete K-ary tree of height H is adjacent. When a new edge between the root and a node ...

We consider a robust shortest path problem when the cost coefficient is the product of two uncertain factors. We first show that the robust problem can be solved in polynomial time by a dual variable enumeration with shortest path problems as subproblems. We also propose a path enumeration approach using a K-shortest paths finding algorithm that may be efficient in many real cases. An applicati...