An improved flow-based formulation and reduction principles for the minimum connectivity inference problem

• Published in: Optimization Vol. 68; no. 10; pp. 1963 - 1983
• Main Authors: Dar, Muhammad Abid, Fischer, Andreas, Martinovic, John, Scheithauer, Guntram
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03.10.2019; Taylor & Francis LLC
• Subjects: Graph theory; Inference; Integer programming; Linear programming; Minimum connectivity inference; Mixed integer; mixed integer linear programming model; Optimization; Reduction; reduction rules; subset interconnection design
• ISSN: 0233-1934; 1029-4945
• DOI: 10.1080/02331934.2018.1465944

The Minimum Connectivity Inference (MCI) problem represents an -hard generalization of the well-known minimum spanning tree problem and has been studied in different fields of research independently. Let an undirected complete graph and finitely many subsets (clusters) of its vertex set be given. Then, the MCI problem is to find a minimal subset of edges so that every cluster is connected with respect to this minimal subset. Whereas, in general, existing approaches can only be applied to find approximate solutions or optimal edge sets of rather small instances, concepts to optimally cope with more meaningful problem sizes have not been proposed yet in literature. For this reason, we present a new mixed integer linear programming formulation for the MCI problem, and introduce new instance reduction methods that can be applied to downsize the complexity of a given instance prior to the optimization. Based on theoretical and computational results both contributions are shown to be beneficial for solving larger instances.