In this paper, we address the problem of broadcasting in a wireless network under a novel communication model: the swamping communication model. In this model, nodes communicate only with those nodes at geometric distance greater than @math and at most @math from them. Communication between nearby nodes under this model can be very time consuming, as the length of the path between two nodes within distance @math is only bounded above by the diameter @math , in many cases. For the @math -node lattice networks, we present algorithms of optimal time complexity, respectively @math for the lattice line and @math for the two-dimensional lattice. We also consider networks of unknown topology of diameter @math and of a parameter @math ( granularity ). More specifically, we consider networks with @math the minimum distance between any two nodes and @math . We present broadcast algorithms for networks of nodes placed on the line and on the plane with respective time complexities @math and @math , where @math .
In 2003, Kuhn, Wattenhofer and Zollinger @cite_8 , introduced a variant of the UDG model handling transmissions and interference separately, named Quasi Unit Disk Graph (Q-UDG) model. In this model, two concentric discs are associated with each station, the smaller representing its communication range and the larger representing its interference range. In our work, we consider a very different situation: as in traditional radio communication models, interference and communication ranges are equal; contrary to previous work, we add the swamping range - a self-interference range - which must be smaller than the communication range.
@cite_8
2065248207
In this paper we study a model for ad-hoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1.We show that .in comparison to the cost known on Unit Disk Graphs .the complexity results in this model contain the additional factor 1 d2. We prove that in Quasi Unit Disk Graphs flooding is an asymptotically message-optimal routing technique, provide a geometric routing algorithm being more efficient above all in dense networks, and show that classic geometric routing is possible with the same performance guarantees as for Unit Disk Graphs if d = 1 v2.