Dominating problems in swapped networks

Swapped Networks (SNs) are a family of two-level interconnection networks, suitable for constructing large parallel and distributed systems. In this paper, the Minimum Dominating Set (MDS) problem and the Minimum Connected Dominating Set (MCDS) problem in SNs are investigated based on the connectivity rule of SNs. We prove the two problems in SNs are NPNP-hard, and present two efficient algorithms for building dominating sets and connected dominating sets in SNs. The proposed algorithms use as input a given (connected) dominating set of the factor network, and yield a good approximation of an MDS or MCDS for the SN provided that the input is a good approximation of an MDS or MCDS for the factor network. We also derive several non-trivial bounds on the (connected) domination parameters of SNs. We believe this work is of theoretical interest in graph theory since SNs form a family of graphs. It may also motivate further research on dominating problems in SNs with their potential applications.