Optimization problems in correlated networks

• Published in: Computational social networks Vol. 3; no. 1; pp. 1 - 20
• Main Authors: Yang, Song, Trajanovski, Stojan, Kuipers, Fernando A.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.01.2016; Springer Nature B.V
• Subjects: Communication networks; Convexity; Correlation analysis; Data-driven Science; Database Management; Formulations; Industrial and Production Engineering; Industrial Organization; Mathematical Models of Cognitive Processes and Neural Networks; Mathematics; Mathematics and Statistics; Media Sociology; Modeling and Theory Building; Optimization; Polynomials; Shortest-path problems; Shortest path; Stochastic link weights; Correlated networks; Min-cut
• ISSN: 2197-4314; 2197-4314
• DOI: 10.1186/s40649-016-0026-y

Background Solving the shortest path and min-cut problems are key in achieving high-performance and robust communication networks. Those problems have often been studied in deterministic and uncorrelated networks both in their original formulations as well as in several constrained variants. However, in real-world networks, link weights (e.g., delay, bandwidth, failure probability) are often correlated due to spatial or temporal reasons, and these correlated link weights together behave in a different manner and are not always additive, as commonly assumed. Methods In this paper, we first propose two correlated link weight models, namely (1) the deterministic correlated model and (2) the (log-concave) stochastic correlated model. Subsequently, we study the shortest path problem and the min-cut problem under these two correlated models. Results and Conclusions We prove that these two problems are NP-hard under the deterministic correlated model, and even cannot be approximated to arbitrary degree in polynomial time. However, these two problems are solvable in polynomial time under the (constrained) nodal deterministic correlated model, and can be solved by convex optimization under the (log-concave) stochastic correlated model.