Algorithms over Dynamic Graphs

Abstract

Graph theory provides mathematical models with computational realizations for a wide range of problems. The classic version provides static models and solutions for these problems. These solutions are often insufficient to versions of the problems in wich the information changes with respect to a continuous variable, eg. time. In the same way one can think on dynamic graphs as graphs in wich some components (arcs, edges, costs) change with respect to a continuous variable. This paper explores graphs with dynamic costs as a bundle, and includes the formulation and the solution for the shortest path problem and the maximum flow problem on these structures. This paper provides an unexplored connection between the dynamic graph theory and the topology, presents approaches to the solution of dynamic versions for the shortest path problem and the maximum flow problem, and proposes both a new source of applications of the metric bundles theory and the type two theory of effectivity.