Let G = (V,E) be an n-nodes non-negatively real-weighted undirected graph. In this paper we show how to enrich a single-source shortest-path tree (SPT) of G with a sparse set of auxiliary edges selected from E, in order to create a structure which tolerates effectively a path failure in the SPT. This consists of a simultaneous fault of a set F of at most f adjacent edges along a shortest path e...

In this paper, we introduce a distributed algorithm for single source shortest path problem for undirected graphs. In this problem, we find the shortest path from a given source node to other nodes in the graph. We start with undirected unweighted graphs in which the shortest path is a path with minimum number of edges. Following, we modify the algorithm to find shortest path for weighted graph...

Abstract. Time-varying network optimization problems have tradition-ally been solved by specialized algorithms. These algorithms have NP-complement time complexity. This paper considers the time-varying short-est path problem, in which can be optimally solved in O(T(m + n)) time,where T is a given integer. For this problem with arbitrary waiting times,we propose an approximation algorithm, whic...

This paper describes and evaluates the performance of various reinforcement learning algorithms with shortest path algorithms that are widely used for routing packets through the network. Shortest path routing is the simplest policy used for routing the packets along the path having minimum number of hops. In high traffic or high mobility conditions, the shortest path get flooded with huge numb...

We discuss the generalization of the point-to-point (and single-source) shortest path problem to instances where the shortest path must satisfy a formal language constraint. We describe theoretical and experimental results on a generalization of Dijkstra’s algorithm to finding regular-language-constrained shortest paths. This algorithm forms a model for single-source shortest paths and point-to...

Understanding how and how far information, behaviors, or pathogens spread in social networks is an important problem, having implications for both predicting the size of epidemics, as well as for planning effective interventions. There are, however, two main challenges for inferring spreading paths in real-world networks. One is the practical difficulty of observing a dynamic process on a netwo...

Numerous algorithms have been proposed to solve the shortest-pathproblem; many of them consider a single-mode network and crispcosts. Other attempts have addressed the problem of fuzzy costs ina single-mode network, the so-called fuzzy shortest-path problem(FSPP). The main contribution of the present work is to solve theoptimum path problem in a multimodal transportation network, inwhich the co...

In this paper we show that a very simple and efficient approach can be used to solve the all pairs almost shortest path problem on the class of weakly chordal graphs and its different subclasses. Moreover, this approach works well also on graphs with small size of largest induced cycle and gives a unified way to solve the all pairs almost shortest path and all pairs shortest path problems on di...

Find a shortest path P with minimum eccentricity, Find a shortest path P with minimum eccentricity,