The Directed Dominating Set Problem: Generalized Leaf Removal and Belief Propagation

A minimum dominating set for a digraph (directed graph) is a smallest set of vertices such that each vertex either belongs to this set or has at least one parent vertex in this set. We solve this hard combinatorial optimization problem approximately by a local algorithm of generalized leaf removal and by a message-passing algorithm of belief propagation. These algorithms can construct near-optimal dominating sets or even exact minimum dominating sets for random digraphs and also for real-world digraph instances. We further develop a core percolation theory and a replica-symmetric spin glass theory for this problem. Our algorithmic and theoretical results may facilitate applications of dominating sets to various network problems involving directed interactions.Comment: 11 pages, 3 figures in EPS forma

Derivation of diagnostic models based on formalized process knowledge

© IFAC.Industrial systems are vulnerable to faults. Early and accurate detection and diagnosis in production systems can minimize down-time, increase the safety of the plant operation, and reduce manufacturing costs. Knowledge- and model-based approaches to automated fault detection and diagnosis have been demonstrated to be suitable for fault cause analysis within a broad range of industrial processes and research case studies. However, the implementation of these methods demands a complex and error-prone development phase, especially due to the extensive efforts required during the derivation of models and their respective validation. In an effort to reduce such modeling complexity, this paper presents a structured causal modeling approach to supporting the derivation of diagnostic models based on formalized process knowledge. The method described herein exploits the Formalized Process Description Guideline VDI/VDE 3682 to establish causal relations among key-process variables, develops an extension of the Signed Digraph model combined with the use of fuzzy set theory to allow more accurate causality descriptions, and proposes a representation of the resulting diagnostic model in CAEX/AutomationML targeting dynamic data access, portability, and seamless information exchange

Merging process models and plant topology

The paper discusses the merging of first principles process models with plant topology derived in an automated way from a process drawing. The resulting structural models should make it easier for a range of methods from the literature to be applied to industrial-scale problems in process operation and design. © 2011 Zhejiang University