Abstract. The shortest paths tree problem consists in finding a spanning tree rooted at a given node, in a directed weighted graph, such that for each node i , the path of the tree which goes from i to the root has minimal weight. We propose an algorithm which is a deterministic version of Howard’s policy iteration scheme. We show that policy iteration is faster than the Bellman (or value itera...

Algorithms to solve probabilistic planning problems can be classified in probabilistic planners and replanners. Probabilistic planners invest significant computational effort to generate a closed policy, i.e., a mapping function from every state to an action, and these solutions never “fail” if the problem correctly models the environment. Alternatively, replanners computes a partial policy, i....

Data coming from real-world applications are very often affected by uncertainty. On the other hand, it is difficult to translate uncertainty in terms of combinatorial optimization. In this paper we study a combinatorial optimization model to deal with uncertainty in arc costs in shortest path problems. We consider a model where feasible arc cost scenarios are described via a convex polytope. We...

The original goal of this project was to investigate and compare the experimental performance and ease of programming of algorithms for geometric shortest path finding using shared memory and message passing programming styles on a shared memory machine. However, due to the extended unavailability of a suitable shared memory machine, this goal was only partially met, though a system suitable fo...

This paper presents a novel formulation for the problem of finding objects in a known environment while minimizing the search cost. Our approach consists in formalizing this class of problems as Stochastic Shortest Path (SSP) problems, a decision-theoretic framework for probabilistic environments. The obtained problems are solved by using offthe-shelf domain-independent probabilistic planners. ...

In this paper, we discuss the relation of unsplittable shortest path routing (USPR) to other routing schemes and study the approximability of three USPR network planning problems. Given a digraph D = (V,A) and a set K of directed commodities, an USPR is a set of flow paths Φ(s,t), (s, t) ∈ K, such that there exists a metric λ = (λa) ∈ Z+ with respect to which each Φ(s,t) is the unique shortest ...

The purpose of this article is to bring together some results on random assignment and shortest path problems, and to clarify how they relate to each other. In particular, we investigate the consequences of the two very different and hard proofs of the ζ(2) limit theorem for the random assignment problem given by David Aldous [1] and by Chandra Nair, Balaji Prabhakar and Mayank Sharma [11]. The...

We consider a stochastic version of the classical shortest path problem whereby for each node of a graph, we must choose a probability distribution over the set of successor nodes so as to reach a certain destination node with minimum expected cost. The costs of transition between successive nodes can be positive as well as negative. We prove natural generalizations of the standard results for ...

We investigate the uncertain versions of two classical combinatorial optimization problems, namely the Single-Pair Shortest Path Problem (SP-SPP) and the Single-Source Shortest Path Problem (SS-SPP). The former consists of finding a path of minimum length connecting two specific nodes in a finite directed graph G; the latter consists of finding the shortest paths from a fixed node to the remain...

In most vehicle routing and crew scheduling applications solved by column generation, the subproblem corresponds to a shortest path problem with resource constraints (SPPRC) or one of its variants. This paper proposes a classification and a generic formulation for the SPPRCs, briefly discusses complex modeling issues involving resources, and presents the most commonly used SPPRC solution method...