The shortest path problem is considered with yet another extension. The transit times b(x,y,u) and the arc costs c(x,y,u) on arc (x,y) vary as a function of the departure time u at the beginning vertex of the arc. The problem considered is to find the shortest path between a pair of nodes such that the total traverse time is lesser than some specified value T. Waiting times at nodes are conside...

We present a modification of the Real-Time Dynamic Programming (rtdp) algorithm that makes it a genuine off-line algorithm for solving Stochastic Shortest-Path problems. Also, a new domainindependent and admissible heuristic is presented for Stochastic Shortest-Path problems. The new algorithm and heuristic are compared with Value Iteration over benchmark problems with large state spaces. The r...

We study the following problem k-constrained shortest path problem: given an acyclic directed graph D = (V,E) with arc weights ci,j , (i, j) ∈ E, two nodes s and t and an integer k, nd a shortest st-path containing at most k arcs. An important application of the problem in linear curve approximation is discussed. Vertices and edges of associated polytopes are determined, and integrality of thes...

Optimal solutions to Stochastic Shortest Path Problems (SSPs) usually require that there exists at least one policy that reaches the goal with probability 1 from the initial state. This condition is very strong and prevents from solving many interesting problems, for instance where all possible policies reach some dead-end states with a positive probability. We introduce a more general and rich...

We consider shortest path problems defined on graphs with random arc costs. We assume that information on arc cost values is accumulated as the graph is being traversed. The objective is to devise a policy that leads from an origin to a destination node with minimal expected cost. We provide dynamic programming algorithms, estimates for their complexity, negative complexity results, and analysi...

We analyze a class of partially observed stochastic shortest path problems. These are terminating Markov decision process with imperfect state information that evolve on an innnite time horizon and have a total cost criterion. For well-posedness, we make reasonable stochastic shortest path type assumptions: (1) the existence of a policy that guarantees termination with probability one and (2) t...

The topic of this lecture is the application of triangulations to shortest path problems. Only simple polygons will be considered. Given two points inside a polygon, the goal is to find the shortest path lying inside the polygon between the two points; see Fig. 1. One can think of the shortest path as a taut string connecting the two points. We begin with some definitions. Let P be a simple pol...

We consider how to use the Bellman residual of the dynamic programming operator to compute suboptimality bounds for solutions to stochastic shortest path problems. Such bounds have been previously established only in the special case that “all policies are proper,” in which case the dynamic programming operator is known to be a contraction, and have been shown to be easily computable only in th...

In this paper we weaken the conditions under which some of the basic analytical and algorithmic results for finite-state stochastic shortest path problems hold. We provide an analysis under three types of assumptions, under all of which the standard form of policy iteration may fail, and other anomalies may occur. In the first type of assumptions, we require a standard compactness and continuit...

Here we present a novel visible analog computing approach for solving a wide class of shortest path problems. Using a microfluidic chip for computation, based on the lighting up of a glow discharge, the solution to maze search problems, the solution of a network shortest path and k-shortest paths problems and the practical application of finding the shortest paths between several landmarks from...