Large Grids and Local Information Flow as a Reason for High Complexity

1. ABSTRACT The analysis of many complex problems and complex dynamical systems shows that there are systematic dependencies between high complexity and the existence of large grids in the underlying structures. This complexity criterion is formulated in a precise way and analysed in different areas of application, particularly for selected industrial and management problems. We discuss how our criterion can be applied to make complex problems more tractable by exploring structural parameters to control the complexity of problems and systems in complexity engineering. In some areas the criterion is provable in a strong mathematical sense, whereas in others it is confirmed by numerous examples, without finding a counterexample. The areas of application cover: complexity theory, design of efficient algorithms, dynamic systems, chaos theory, neural networks, auctions, capital markets, design of VLSI-circuits, software engineering and risk management.

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