Given a dynamic network with n nodes and m arcs in which all attributes including travel times, travel costs and waiting costs may change dynamically over a time horizon T. The dynamic shortest path problem is to determine a path from a specified source node to every other node with minimal total cost, subject to the constraint that the total traverse time is at most T. This problem can be form...

Consider the problem of finding the shortest paths from a node source s to a node sink t in a complete network. On any given instance of the problem, only a subset of the intermediate nodes can be used to go from s to t , the subset being chosen according to a given probability law. We wish to find an a priori path from s to f such that, on any given instance of the problem, the sequence of nod...

Suppose you have to route agents through a network from a source node to a destination node in some optimal way; for instance by minimizing the total travel cost. Nothing new up to now – you could use a standard shortestpath algorithm. Suppose, however, that you want to avoid pure deterministic routing policies in order, for instance, to allow some exploration of the network, to avoid congestio...

Sequencing activities over time is a fundamental optimization problem. The problem can be modeled using a directed network in which activities are represented by nodes and pairs of activities that can be performed consecutively are represented by arcs. A sequence of activities then corresponds to a path in the directed network, and an optimal sequence of activities, assuming appropriately chose...

Symbolic computation techniques play a fundamental role in these days logic synthesis and formal hardware veriication algorithms. Recently, Algebraic Decision Diagrams, i.e., BDD's with a set of constant values diierent than the set f0; 1g, have been used to solve general purpose problems, such as matrix multiplication, shortest path calculation, and solution of linear systems, as well as logic...

Shortest path problems occupy an important position in Operations Research as well as in Artificial Intelligence. In this paper we study shortest path algorithms that exploit heuristic estimates. The well-known algorithms are put into one framework. Besides we present an interesting application of binary numbers in the shortest path theory.

In this paper, we address a shortest path problem where an autonomous vehicle moves on a polyhedral surface according to a distance function that depends on the direction of the movement (directional) and on the friction of the space (frictional). This shortest path problem generalizes a hierarchy of problems and finds geometric structure to solve several proximity problems. We perform the char...

The travelling salesman problem is to find a shortest path from the travelling salesman’s hometown, make the round of all the towns in the set, and finally go back home. This paper investigates the travelling salesman problem with fuzzy random travelling time. Three concepts are proposed: expected shortest path, (α, β)-path and chance shortest path according to different optimal desire. Corresp...

Shortest path problem is a fundamental problem in network optimization and combinational optimization. The existing literature mainly concerned with the problem in deterministic, stochastic or fuzzy environments by using different tools. Different from the existing works, we investigate shortest path problem by regarding arc lengths as uncertain variables which are employed to describe the beha...

we give an algorithm, called t*, for finding the k shortest simplepaths connecting a certain pair of nodes, s and t, in a acyclic digraph.first the nodes of the graph are labeled according to the topologicalordering. then for node i an ordered list of simple s − i paths iscreated. the length of the list is at most k and it is created by usingtournament trees. we prove the correctness of t* and ...