The inverse shortest path problem is to minimize the modification on the edge weights such that a predetermined path becomes the shortest one from the origin to the destination with respect to the new edge weights. In this paper, the inverse shortest path problem is considered on a graph with uncertain edge weights. It is shown that the model of the uncertain inverse shortest path problem can b...

This paper considers the general capacity expansion path problem (GCEP) for the telecommunication operators. We investigate the polynomial equivalence between the GCEP problem and the constrained shortest path problem (CSP) and present a pseudopolynomial algorithm for the GCEP problem, no matter the graph is acyclic or not. Furthermore, we investigate two special versions of the GCEP problem. F...

The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the quadratic shortest path problem with a matrix variable of order m + 1, where m is the number of arcs in the graph. We use the alternating direction method of...

Received 17September 2013; accepted 5 October2013 L Baba Abstract. Finding shortest paths in graphs has been the area of interest for many researchers. Shortest paths are one of the fundamental and most widely used concepts in networks. In this paper the authors present an algorithm to find an Intuitionistic Fuzzy Shortest Path (IFSP) in a directed graph in which the cost of every edges are rep...

Cellular Automata (CAs) are computational models that can capture the essential features of systems in which global behavior emerges from the collective effect of simple components, which interact locally. During the last decades, CAs have been extensively used for mimicking several natural processes and systems to find fine solutions in many complex hard to solve computer science and engineeri...

Finding the shortest path in a directed graph is one of the most important combinatorial optimization problems, having applications in a wide range of fields. In its basic version, however, the problem fails to represent situations in which the value of the objective function is determined not only by the choice of each single arc, but also by the combined presence of pairs of arcs in the solut...

In this class project, we investigate certain aspects of the Weight Constrained Shortest Path Problem. The problem is known NP-Hard, but there are algorithms, both exact and approximate, that attempt to solve it. We analyze two of the important exact methods label setting on graphs and Lagrangean relaxation of the constraint, and evaluate how they perform with different graph sizes, and differe...

The shortest path problem in which the (s, t)-paths P of a given digraph G = (V,E) are compared with respect to the sum of their edge costs is one of the best known problems in combinatorial optimization. The paper is concerned with a number of variations of this problem having different objective functions like bottleneck, balanced, minimum deviation, algebraic sum, k-sum and k-max objectives,...