Abstract
<jats:p>This paper addresses the problem of reducing control (service) traffic in mobile Ad Hoc networks through topology control. A novel approach based on matroid theory is proposed for constructing a reduced network structure. The network is modeled as an undirected graph, where a graphical matroid is defined, and the optimization problem is formulated as the search for a minimum spanning tree representing a matroid basis. A centralized topology control algorithm is developed, providing minimization of the total communication cost while preserving network connectivity. In addition, a distributed version of the algorithm is proposed, which relies on local neighbor information and is suitable for dynamic network environments. The proposed matroid-based approach enables a significant reduction in control traffic without substantial degradation of key performance metrics, such as packet delivery ratio and end-to-end delay. The results demonstrate the applicability of the method for improving routing efficiency in mobile Ad Hoc networks. Keywords: Ad Hoc networks, control traffic, matroid theory, minimum spanning tree, routing, topology control</jats:p>