Abstract-In the minimum energy broadcasting problem, each node can adjust its transmission power in order to minimize total energy consumption but still enable a message originated from a source node to reach all the other nodes in an ad-hoc wireless network. In all existing solutions each node requires global network information (including distances between any two neighboring nodes in the network) in order to decide its own transmission radius. In this paper, we describe a new localized protocol where each node requires only the knowledge of its distance to all neighboring nodes and distances between its neighboring nodes (or, alternatively, geographic position of itself and its neighboring nodes). In addition to using only local information, our protocol is shown experimentally to be comparable to the best known globalized BIP solution. Our solutions are based on the use of relative neighborhood graph which preserves connectivity and is defined in localized manner.

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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.

The theorem stating that the family of frontiers of recognizable tree languages is exactly the family of context-free languages (see J. Mezei and J. B. Wright, 1967, Inform. and Comput. 11, 3 29), is a basic result in the theory of formal languages. In this article, we prove a similar result: the family of frontiers of recognizable picture languages is exactly the family of context-sensitive languages. ] 1997 Academic Press