On the morphological structure of a network

Abstract

In literature, both topological and resource-related measures are used to predict the difficulty of a project scheduling problem. Rapid progress regarding solution procedures has resulted in the development of a number of data generators in order to generate instances under a controlled design and in different standard sets with problem instances. These complexity measures need to serve as predictors for the complexity of the problem under study. In this paper, we report on results for the topological structure of a network. The contribution of this paper is threefold. First, we review six topological network indicators in order to describe the structure of a network in a detailed way. These indicators were originally developed by [20] and have been modified or sometimes completely replaced by alternative indicators in order to give a better description of the topology of a network. Secondly, we generate a large amount of different networks with four network generators. This allows us to draw conclusions on both the performance of different network generators and to give a critical remark on well-known datasets from literature. Our general conclusions are that none of the network generators are able to capture the complete feasible domain of all networks. Moreover, each network generator covers its own network-specific domain and, consequently, contributes to the generation of instance data sets. Finally, we perform computational results on the well-known resource-constrained project scheduling problem to proof that our indicators are reliable and have significant predictive power to serve as complexity indicators. Keywords: Networks, Topological structure, Graphs, Project Scheduling instances