Enhancing Reliability of Folded Petersen Networks Based on Edge Partition.

The rapid expansion of infrastructure topology, especially noticeable in high-performance computing systems and data center networks, significantly increases the likelihood of failures in network components. While traditional (edge) connectivity has long been the standard for measuring the reliability of interconnection networks, this approach becomes less effective as networks grow more complex. To address this, two innovative metrics, named matroidal connectivity and conditional matroidal connectivity, have emerged. These metrics provide the flexibility to impose constraints on faulty edges across different dimensions and have shown promise in enhancing the edge fault tolerance of interconnection networks. In this paper, we explore (conditional) matroidal connectivity of the k-dimensional folded Petersen network FPk, which is constructed by iteratively applying the Cartesian product operation on the well-known Petersen graph and possesses a regular, vertex- and edge-symmetric architecture with optimal connectivity and logarithmic diameter. Specifically, the faulty edge set F is partitioned into k subsets according to the dimensions of FPk. We then arrange these subsets by their cardinality, imposing the restriction whereby the cardinality of the ith largest subset dose not exceed 3 ⋅ 10i−1 for 1 ≤ i ≤ k. Subsequently, we show that FPk − F is connected with |F|≤∑i=1k(3 ⋅ 10i−1) and determine the exact value of matroidal connectivity and conditional matroidal connectivity. [ABSTRACT FROM AUTHOR]