We address the problem for finding the K best path trees connecting a source node with any other non-source node in a directed network with arbitrary lengths. The main result in this paper is the proof that the kth shortest path tree is adjacent to at least one of the previous (k−1) shortest path trees. Consequently, we design an O(+Km) time and O(K+m) space algorithm to determine the K shortes...

This paper considers a stochastic version of the shortest path problem, the Distributionally Robust Stochastic Shortest Path Problem(DRSSPP) on directed graphs. In this model, the arc costs are deterministic, while each arc has a random delay. The mean vector and the second-moment matrix of the uncertain data are assumed known, but the exact information of the distribution is unknown. A penalty...

We give a randomized parallel algorithm for computing single-source shortest paths in weighted digraphs. We show that the exact shortest-path problem can be efficiently reduced to solving a series of approximate shortest-path subproblems. Our algorithm for the approximate shortest-path problem is based on the technique used by Ullman and Yannakakis in a parallel algorithm for breadth-first sear...

In graph theory, the shortest path problem is the problem of finding a path between two vertices in a graph such that the sum of the weights of its edges is minimized. In last semester's report "Distributed Systems seminar: Shortest-path problem[1]" the previously created program was introduced that was able to perform shortest path search using A* algorithm on OpenStreetmap data. There were ma...

Biswas, S. S. , Alam, B. , Doja, M. N. 2013. An algorithm for extracting intuitionistic fuzzy shortest path in a graph. Applied Computational Intelligence and Soft Computing, 17. Dubois, D. and Prade, H. 1980. Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York. De, P. K. and Das, D. 2012 Ranking of trapezoidal intuitionistic fuzzy numbers, Intelligent Systems Design and A...

The shortest path problem is one of the most fundamental problems in network optimization. This paper is concerned with shortest path problems in non-deterministic environment, in which the lengths of some arcs have stochastic characteristics and meanwhile some have uncertain characteristics. In order to investigate paths in these networks, this paper introduces the chance distribution of minim...

This paper presents new heuristic algorithms using the guided A* search method : Guided Minimum Detour (GMD) algorithm and Line-by-Line Guided Minimum Detour (LGMD) algorithm for finding optimal rectilinear (L,) shortest paths in the presence of rectilinear obstacles. The GMD algorithm runs O(nhr(1ogN) + tN) in time and takes O(N) in space, where N is the number of extended line segments includ...

This main purpose of this paper is to develop an algorithm to find the shortest path on a network in which the weights of the edges are represented by bipolar neutrosophic numbers. Finally, a numerical example has been provided for illustrating the proposed approach. Introduction Smarandache [1, 2] introduced neutrosophic set and neutrosophic logic by considering the nonstandard analysis. The c...

This paper considers a stochastic version of the shortest path problem, the Stochastic Shortest Path Problem with Delay Excess Penalty on directed, acyclic graphs. In this model, the arc costs are deterministic, while each arc has a random delay, assumed normally distributed. A penalty occurs when the given delay constraint is not satisfied. The objective is to minimize the sum of the path cost...

Given an n-vertex and m-edge non-negatively real-weighted graph G = (V, E, w), whose vertices are partitioned into a set of k clusters, a clustered network design problem on G consists of finding a (possibly optimal) solution to a given network design problem on G, subject to some additional constraint on its clusters. In this paper, we focus on the classic shortest-path tree problem and summar...