In this lecture, we will further examine shortest path algorithms. We will first revisit Dijkstra’s algorithm and prove its correctness. Next, we will look at another shortest path algorithm known as the Bellman-Ford algorithm, that has a slower running time than Dijkstra’s but allows us to compute shortest paths on graphs with negative edge weights. Lastly, we look at an O(n3)-time algorithm f...

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.

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 ...

We provide several new algorithmic results for the secluded path problem, specifically approximation and optimality results for the static algorithm of [3, 5], and an extension (h-Memory) of it based on de Bruijn graphs, when applied to bounded degree graphs and some other special graph classes which can model wireless communication and line-of-sight settings. Our primary result is that h-Memor...

We give an algorithm to compute a (Euclidean) shortest path in a polygon with h holes and a total of n vertices. The algorithm uses O(n) space and requires O(n + h 2 log n) time.

We study acceleration methods for point-to-point shortest path and constrained shortest path computations in directed graphs, in particular in road and railroad networks. Our acceleration methods are allowed to use a preprocessing of the network data to create auxiliary information which is then used to speed-up shortest path queries. We focus on two methods based on Dijkstra’s algorithm for sh...

We consider biobjective shortest path problems in networks with fuzzy arc lengths. Considering the available studies for single objective shortest path problems in fuzzy networks, using a distance function for comparison of fuzzy numbers, we propose three approaches for solving the biobjective prob- lems. The rst and second approaches are extensions of the labeling method to solve the sing...

During the last years, impressive progress has been achieved in the field of algorithm engineering. A problem becoming more and more important is that of data dependency: the performance of an algorithm often highly depends on the input. Yet, for a given input, it is highly non-trivial to select the best solving strategy. In this work, we introduce a new methodology for evaluating speed-up tech...

There exit several high speed computation applications that requires minimum distance computation between nodes in weighted graph. Dedicated techniques exist for this purpose are called as shortest path computation. Depending upon need of application, there are three type of shortest path problems; Single Source Shortest Path (SSSP), Single Destination Shortest Path (SDSP) and All Pair Shortest...