Connected Dominating Sets in Wireless Networks with Different Transmission Ranges

Abstract

Abstract-Since there is no fixed infrastructure or centralized management in wireless ad hoc networks, a Connected Dominating Set (CDS) has been proposed to serve as a virtual backbone. The CDS of a graph representing a network has a significant impact on the efficient design of routing protocols in wireless networks. This problem has been studied extensively in Unit Disk Graphs (UDG), in which all nodes have the same transmission ranges. However, in practice, the transmission ranges of all nodes are not necessarily equal. In this paper, we model a network as a disk graph and introduce the CDS problem in disk graphs. We present two efficient approximation algorithms to obtain a minimum CDS. The performance ratio of these algorithms is constant if the ratio of the maximum transmission range over the minimum transmission range in the network is bounded. These algorithms can be implemented as distributed algorithms. Furthermore, we show a size relationship between a maximal independent set and a CDS as well as a bound of the maximum number of independent neighbors of a node in disk graphs. The theoretical analysis and simulation results are also presented to verify our approaches.

An energy-aware distributed algorithm for virtual backbone in wireless sensor network with different transmission range

“…Thai and colleagues [3] have provided based on MIS an algorithm for finding CDS in DGB. This article is the first article that specifically deals with the DGB.…”

“…For the second phase should MIS nodes connected to each other and we have to do is use the minimum number of connecting nodes according to the performance Steiner tree [3] …”

“…The following three important properties are listed in [3] for CDS in DGB Proof: The algorithm has two phases; the first phase of MIS construction and the second phase is the construction of CDS. From Lemma 3 approximation ratio of the first phase (MIS) is Kopt and from Theorem 2, approximation ratio the second phase is less than Kopt then result the approximation ratio of algorithm is less than the 2 Kopt, thus algorithm has approximately constant approximation ratio.…”

“…In this model, all nodes have the same transmission range and two other neighboring nodes within range if they are transmission range to each other. Since in practice the assumption that all nodes have the same transmission range due to the weakening of transmitterreceiver and many other factors is impossible, and in many applications require different transmission range are, in this paper, a model of the DGB (Disk Graph with Bidirectional links) we use [3] where nodes can adopt a different transmission range.…”

A New Algorithm for Finding Trees with Many Leaves

“…Being a problem that has many practical applications, e.g., in network design [10,18,21,24], it is already widely studied with regard to its complexity and approximability. All versions are APX-hard [15] and there is a polynomial time 2-approximation for undirected graphs [23] and a 3-approximation in almost linear time [20].…”