Achieving Dilution without Knowledge of Coordinates in the SINR Model

Considerable literature has been developed for various fundamental distributed problems in the SINR (Signal-to-Interference-plus-Noise-Ratio) model for radio transmission. A setting typically studied is when all nodes transmit a signal of the same strength, and each device only has access to knowledge about the total number of nodes in the network $n$, the range from which each node's label is taken $[1,\dots,N]$, and the label of the device itself. In addition, an assumption is made that each node also knows its coordinates in the Euclidean plane. In this paper, we create a technique which allows algorithm designers to remove that last assumption. The assumption about the unavailability of the knowledge of the physical coordinates of the nodes truly captures the `ad-hoc' nature of wireless networks. Previous work in this area uses a flavor of a technique called dilution, in which nodes transmit in a (predetermined) round-robin fashion, and are able to reach all their neighbors. However, without knowing the physical coordinates, it's not possible to know the coordinates of their containing (pivotal) grid box and seemingly not possible to use dilution (to coordinate their transmissions). We propose a new technique to achieve dilution without using the knowledge of physical coordinates. This technique exploits the understanding that the transmitting nodes lie in 2-D space, segmented by an appropriate pivotal grid, without explicitly referring to the actual physical coordinates of these nodes. Using this technique, it is possible for every weak device to successfully transmit its message to all of its neighbors in $\Theta(\lg N)$ rounds, as long as the density of transmitting nodes in any physical grid box is bounded by a known constant. This technique, we feel, is an important generic tool for devising practical protocols when physical coordinates of the nodes are not known.Comment: 10 page

Enhanced termination condition for deterministic broadcasting protocols in mobile ad hoc networks

Deterministic approach to broadcasting in Mobile Ad Hoc Networks (MANETs) is effective in reducing redundant broadcasting. In this approach, a transmitting node selects a subset of its immediate or 1-hop neighbors to rebroadcast the message such that all its 2-hop neighbors will receive the message, or being covered. In order to reduce redundant broadcasting, the set of 1-hop neighbors to be covered should be reduced as much as possible. Another important aspect that affects the effectiveness of a deterministic broadcasting protocol is the termination condition that inhibits a node from transmitting a particular message unnecessarily. However, existing termination conditions are not optimized. We propose a new covered/uncovered termination condition where each node is assigned with covered/uncovered status. In this paper, we show that our covered/uncovered termination condition ensures full network coverage, does not incur any control message overhead, and yet requires the least number of rebroadcasting nodes. When we apply the termination condition to some existing deterministic broadcasting protocols, the saving in the number of broadcasting nodes can be as significant as 45% when there are 100 nodes randomly distributed in an area of 1000 x 1000 m2. ©2010 IEEE.published_or_final_versionThe 72nd IEEE Vehicular Technology Conference (VTC 2010-Fall), Ottawa, ON., 6-9 September 2010. In Proceedings of the IEEE-VTS Vehicular Technology Conference, 2010, p. 1-