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 ...

In this article, we study the problem of finding the next-to-shortest path in circular-arc graph. A next-to-shortest path between any pair of vertices in a shortest path amongst all paths between those vertices with length strictly greater than the length of the shortest path. The next-to-shortest path problem in a directed graph in NP-hard. Here we deigned a polynomial time algorithm to solve ...

We study the shortest-path broadcast problem in graphs and digraphs, where amessage has to be transmitted from a source node s to all the nodes along shortest paths, in the classical telephonemodel. For both graphs and digraphs, we show that the problem is equivalent to the broadcast problem in layered directed graphs. We then prove that this latter problem is NP-hard, and therefore that the sh...

Routing systems have become very attractive recently. They aim to help users on finding out the optimal path to their destinations regarding travel distance, travel time, and other criteria. This paper presents a distributed architecture for networking systems which proposes a new algorithm called Coolest path, which enables multi-criteria personalization based on travel distance, travel time, ...

We consider the problem of computing shortest paths through a dynamic network – a network with time-varying characteristics, such as arc travel times and costs, which are known for all values of time. Many types of networks, most notably transportation networks, exhibit such predictable dynamic behavior over the course of time. Dynamic shortest path problems are currently solved in practice by ...

We introduce the following notion: a digraph D = (V,A) with arc weights c : A → R is called nearly conservative if every negative cycle consists of two arcs. Computing shortest paths in nearly conservative digraphs is NP-hard, and even deciding whether a digraph is nearly conservative is coNP-complete. We show that the “All Pairs Shortest Path” problem is fixed parameter tractable with various ...

This paper is a state of the art on the shortest path problems for which it exists uncertainty and inaccuracy factors on arc values. Two uncertainty models are distinguished: the so-called interval model and the discrete set of scenarios model. Different measures and approaches of robustness are presented: those coming from decision theory, those coming from multicriteria analysis and those com...