The r-Neighborhood Graph: An Adjustable Structure for Topology Control in Wireless Ad Hoc Networks

Abstract

In wireless ad hoc networks, constructing and maintaining a topology with lower node degrees is usually intended to mitigate excessive traffic load on wireless nodes. However, keeping lower node degrees often prevents nodes from choosing better routes that consume less energy. Therefore, the trade-off is between the node degree and the energy efficiency. In this paper, an adjustable structure, named the r-neighborhood graph, is proposed to control the topology. This structure has the flexibility to be adjusted between the two objectives through a parameter r, 0 r 1. More explicitly, for any set of n nodes, the maximum node degree and power stretch factor can be bounded from above by some decreasing and increasing functions of r, respectively. Specifically, the bounds can be constants in some ranges of r. Even more, the r-neighborhood graph is a general structure of both RNG and GG, two well-known structures in topology control. Compared with Y G k , another famous adjustable structure, our method always results in a connected planar with symmetric edges. To construct this structure, we investigate a localized algorithm, named PLA, which consumes less transmitting power during construction and executes efficiently in Oðn log nÞ time.Index Terms-Wireless ad hoc networks, topology control, energy-efficient, localized algorithm. Ç 1 INTRODUCTIONW IRELESS ad hoc networks enhance the conventional deployment of communicating environments for many applications, such as conferences, hospitals, battlefields, search and rescue teams, etc. In these environments, the performance of network operations heavily depends upon the underlying topology [4]. For instance, the delivery rate would be significantly lower as the underlying topology breaks. Therefore, appropriately controlling the topology is a crucial stage in communication. The topology control problem in wireless ad hoc networks has been widely studied in recent years [3], [15], [18], [19], [20], [23], [29], [32]. Generally speaking, the core of this problem is to determine a set of wireless links such that the composed topology is able to achieve certain goals [23]. These goals would be variant depending upon the circumstances and could be either qualitative features or quantitative objectives. Since wireless nodes usually struggle with limited bandwidth and computation power, a genius way should be able to simultaneously achieve several goals. In this paper, we aim to control the topology with the following goals, which are extremely desired in wireless environments:

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