Genetic Algorithms for Vertex Splitting in DAGs

Directed Acyclic Graphs are often used to model circuits and networks. The path length in such Directed Acyclic Graphs represents circuit or network delays. In the vertex splitting problem, the objective is to determine a minimum number of vertices from the graph to split such that the resulting graph has no path of length greater than a given δ. The problem has been proven to be NP-hard. A Genetic Algorithm is used to solve the DAG Vertex Splitting Problem. This approach uses a variable string length to represent the vertices that split the graph and a dynamic population size. The focus of this paper is the comparison of two methods to reduce the string length and of two stepping methods to explore the search space. Experimental results have shown that the multiple binary stepping method outperforms the linear stepping method in yielding better solutions

Parallel Genetic Algorithms for the DAG Vertex Splitting Problem

Directed Acyclic Graphs are often used to model circuits and networks. The path length in such Directed Acyclic Graphs represents circuit or network delays. In the vertex splitting problem, the objective is to determine a minimum number of vertices from the graph to split such that the resulting graph has no path of length greater than a given δ. The problem has been proven to be NP-hard. A Sequential Genetic Algorithm has been developed to solve the DAG Vertex Splitting Problem. Unlike a standard Genetic Algorithm, this approach uses a variable chromosome length to represent the vertices that split the graph and a dynamic population size. Two String Length Reduction Methods to reduce the string length and two Stepping Methods to explore the search space have been developed. Combinations of these four methods have been studied and conclusions are drawn. A parallel version of the sequential Genetic Algorithm has been developed. It uses a fully distributed scheme to assign different string lengths to processors. A ring exchange method is used in order to exchange good individuals between processors. Almost linear speed-up and two cases of super linear speed-up are reported