S-grid: A new quorum-based power saving protocol to maximize neighbor sensibility

Several quorum-based protocols are proposed for multi-hop ad hoc networks like grid, cycling, torus, e-torus and finite projective plane (FPP). All these methods have a low expected quorum overlap size (EQOS) and consequently provide low neighbor sensibility. In this paper we propose a new quorum system called stepped grid (s-grid) which has two different forms: the s-grid(t × w) when t ≠ w and s-grid(n) when t = w = √n. Despite of the grid which has the maximum EQOS of 4, the s-grid has no upper bound. Another weakness of all the above-mentioned quorum systems is the limitation of system size. for example, the grid works with just √n × √n arrays, the torus works with just t × w arrays when w = 2t, the cyclic and the FPP can only be constructed when n = k(k − 1) + 1 and k − 1 is a prime power, but the s-grid(t × w) is very flexible and works with any array size. We derive the EQOS values for the s-grid(t × w) as well as the s-grid(n) and compare our results with the EQOS values of all the above-mentioned quorum systems by analysis. Analyses results show that the s-grid(t × w) and the s-grid(n) have comparably high EQOS values and consequently better neighbor sensibility than the FPP, grid, cyclic, torus and e-torus quorum systems.