节点位置随机的无线自组网中的边界干扰
Bounding Interference in Wireless Ad Hoc Networks with Nodes in Random Position
摘要：
无线节点s处的干扰可以通过其传输范围覆盖s的无线节点的数量来建模。给定无线节点的一组位置，干扰最小化问题是为每个节点分配传输半径（等效地，功率电平），使得所得到的通信图是连接的，同时最小化最大干扰。我们考虑由von Rickenback等人（2005）引入的模型，其中每个传输范围由球表示，并且通信图中的边是对称的。该问题在二维中是NP完全的（Buchin 2008），并且没有已知的多项式时间近似算法。此外，即使在一维（高速公路模型）中，问题的复杂性也是未知的，并且一组n个无线节点的最大干扰可以高达Theta（sqrt（n））（von Rickenback等人，2005）。在本文中，我们将展示如何有效地解决这个问题，在典型的无线ad hoc网络的设置。特别是，我们表明，如果节点的位置是由一组P的n个点均匀和独立地随机选择在一个d维矩形区域，对于任何固定的d，那么由关闭的欧氏最小生成树的P的拓扑结构具有最大的干扰O（log n）的概率很高。我们扩展到一个一般类的通信图在一个广泛的概率分布。接下来，我们提出了一个本地算法，从这个类构建一个图，这是第一个本地算法提供一个上限的预期最大干扰。最后，我们讨论了我们的算法与一套模拟结果的实证评估。
英文摘要：
The interference at a wireless node s can be modelled by the number of wireless nodes whose transmission ranges cover s. Given a set of positions for wireless nodes, the interference minimization problem is to assign a transmission radius (equivalently, a power level) to each node such that the resulting communication graph is connected, while minimizing the maximum interference. We consider the model introduced by von Rickenback et al. (2005), in which each transmission range is represented by a ball and edges in the communication graph are symmetric. The problem is NP-complete in two dimensions (Buchin 2008) and no polynomial-time approximation algorithm is known. Furthermore, even in one dimension (the highway model), the problem's complexity is unknown and the maximum interference of a set of n wireless nodes can be as high as Theta(sqrt(n)) (von Rickenback et al. 2005). In this paper we show how to solve the problem efficiently in settings typical for wireless ad hoc networks. In particular, we show that if node positions are represented by a set P of n points selected uniformly and independently at random over a d-dimensional rectangular region, for any fixed d, then the topology given by the closure of the Euclidean minimum spanning tree of P has maximum interference O(log n) with high probability. We extend this bound to a general class of communication graphs over a broad set of probability distributions. Next we present a local algorithm that constructs a graph from this class; this is the first local algorithm to provide an upper bound on the expected maximum interference. Finally, we discuss an empirical evaluation of our algorithm with a suite of simulation results.
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