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In this paper, we study broadcasting protocols where nodes use some of their neighbors to forward messages. We propose a new protocol based on a variant of neighbor elimination scheme using RNG graph to ensure a full coverage of the network. The computation of RNG uses two kinds of distance: a geometrical one and and neighborhood-based distance that permits to use our protocol without positioning system. This protocol, called RRS for RNG Relay Subset, provides a self-selecting forwarding neighbor operating mode which guarantees a fair broadcast loading. In RRS a node v is a relay for a node u if and only if v is a neighbor of u and v has a RNG-neighbor which is not covered by u transmission. Moreover, experiments with 802.11-like MAC layer show that RRS is efficient.