The shortest path (SP) problem in a network with nonnegative arc lengths can be solved easily by Dijkstra’s labeling algorithm in polynomial time. In the case of significant uncertainty of the arc lengths, a robustness approach is more appropriate. In this paper, we study the SP problem under arc length uncertainties. A scenario approach is adopted to characterize uncertainties. Two robustness ...

The Minimum Eccentricity Shortest Path Problem consists in finding a shortest path with minimum eccentricity given undirected graph. problem is known to be NP-complete and W[2]-hard respect the desired eccentricity. We present fpt-algorithms for parameterized by modular width, distance cluster graph, combination of treewidth eccentricity, maximum leaf number.

  The traveling salesman problem is a well-known and important combinatorial optimization problem. The goal of this problem is to find the shortest Hamiltonian path that visits each city in a given list exactly once and then returns to the starting city. In this paper, for the first time, the shortest Hamiltonian path is achieved for 1071 Iranian cities. For solving this large-scale problem, tw...

Open shortest path first is the most commonly used intera-domain routing protocol. It selects the paths which traffic is routed within autonomous systems. OSPF calculates routes as follow. Each link is assigned weights by operator. Each node within the autonomous system computes shortest paths and creates destination tables to route data to next node along the path to its destination. Shortest ...

This paper concerns a variant of the multi-goal path planning problem in which goals may be polygonal regions. The problem is to find a closed shortest path in a polygonal map such that all goals are visited. The proposed solution is based on a self-organizing map algorithm for the traveling salesman problem, which is extended to the polygonal goals. Neurons’ weights are considered as nodes ins...

We consider the biobjective shortest path (BSP) problem as the natural extension of the single objective shortest path problem. BSP problems arise in various applications where networks usually consist of large numbers of nodes and arcs. Since obtaining the set of efficient solutions to a BSP problem is more difficult (i.e. NP-hard and intractable) than solving the corresponding single objectiv...

This article provides an overview of the performance and the theoretical complexity of approximate and exact methods for various versions of the shortest path problem. The proposed study aims to improve the resolution of a more general covering problem within a column generation scheme in which the shortest path problem is the sub-problem.

Network flow problems form a core area of Combinatorial Optimization. Their significance arises both from their very large number of applications and their theoretical importance. This thesis focuses on efficient exact algorithms for network flow problems in P and on approximation algorithms for NP -hard variants such as disjoint paths and unsplittable flow. Given an n-vertex, m-edge directed n...

A class of cooperative games arising from shortest path problems is deened. These shortest path games are shown to be totally balanced and allow a population-monotonic allocation scheme. Possible methods for obtaining core elements are indicated; rst, by relating to the allocation rules in taxation and bankruptcy problems, second, by constructing an explicit rule that takes opportunity costs in...