“…Moreover, it is very conservative because it guesses its connectivity instead of measuring it directly, which results in less energy savings (Roychowdhury and Patra, 2010). To this end, some versions seem to exceed these limits such as the diagonal GAF (DGAF) protocol which allows direct communication between two diagonal grids (Shang and Liu, 2012), two-level GAF (TGAF) that overcome the problem of communication between only neighboring grids (Vaibhav and Dheeresh, 2015), optimized GAF that improve transitions between node states (Grover et al , 2014b), dislocated grid GAF (GAFDG) that help overcome the problem of limited energy (Zu-jue et al , 2012), hierarchical GAF (HGAF) which also improve energy efficiency by increasing cell size, and using a layered structure in each cell to select active nodes (Inagaki and Ishihara, 2009; Aznaoui et al , 2021a), cooperative agents GAF (CAGAF) that improve routing path to reduce energy consumed (Aznaoui et al , 2019), etc. Given the limitations of GAF protocol and its many improved versions to overcome the problems encountered in the wireless communication sector, we propose an enhanced version of GAF based on the theory of graphs, linear mathematical programming and data aggregation to save and reduce energy consumption and extend the network lifetime.…”