Shortest path computation is a classical combinatorial optimization problem. Neural networks, as a class of effective optimization approaches, have been used for processing path optimization problems for a long time. Pulse Coupled Neural Network (PCNN) is a very different neural network, which has also been proposed to compute shortest paths in recent years. In some existing PCNN models, the co...

Finding shortest paths and shortest distances between points on a surface S in three-dimensional space is a well-studied problem in differential geometry and computational geometry. The shortest path between two points on S is denoted a geodesic path on the surface and the shortest distance between two points on S is denoted a geodesic distance. In this survey, we consider the case where a disc...

The motion planning problems for non-holonomic car-like robots have been extensively studied in the literature. The curvature-constrained shortest-path problem is to plan a path (from an initial connguration to a nal connguration, where a connguration is deened by a location and an orientation) in the presence of obstacles, such that the path is a shortest among all paths with a prescribed curv...

We consider a generalization of the shortest-path problem: given an alphabet Σ, a graph G whose edges are weighted and Σ-labeled, and a regular language L ⊆ Σ∗, the L-constrained shortest-path problem consists of finding a shortest path p in G such that the concatenated labels along p form a word of L. This definition allows to model, e. g., many traffic-planning problems. We present extensions...

Multimedia communications have become popular in many network services, such as video conferencing, video on demand, and so on. Most multimedia applications require that the attached hosts/routers transmit data through multicasting. In order to provide efficient data routing, routers must provide the multicast capability. In this paper, a self-feedback mechanism controlled by an annealing strat...

We consider generalized shortest path problems with cost and weight functions for the arcs of a graph. According to their weight arcs may generate or consume ow. Weights may be additive or multiplicative on a path. More precisely, if x units enter an arc a = (u; v) then x + w(a) resp. x w(a) leave it. The cost is charged per unit and summed over the edges of a path. If the weights multiply, the...

This paper studies the asymptotic behavior of several continuous-time dynamical systems which are analogs of ant colony optimization algorithms that solve shortest path problems. Local asymptotic stability of the equilibrium corresponding to the shortest path is shown under mild assumptions. A complete study is given for a recently proposed model called EigenAnt: global asymptotic stability is ...

Nowadays most data networks use shortest path protocols such as OSPF or IS-IS to route traffic. Given administrative routing lengths for the links of a network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. One of the most fundamental problems in planning shortest path networks is to decide whether a given set of routing pat...

We consider recently-derived error bounds that can be used to bound the quality of solutions found by heuristic search algorithms for stochastic shortest path problems. In their original form, the bounds can only be used for problems with positive action costs. We show how to generalize the bounds so that they can be used in solving any stochastic shortest path problem, regardless of cost struc...