Connected dominating sets in disk graphs with bidirectional links

In this paper, we study the connected dominating set (CDS) problem in disk graphs. The CDS problem has a significant impact on an efficient design of routing protocols in wireless networks. This problem has been studied extensively in unit disk graphs, in which each node has the same transmission range. However, in wireless ad hoc networks, the transmission ranges of all nodes are not necessary equal. In this paper, we introduce the CDS problem in disk graphs and present a constant approximation algorithm which can be implemented as a distributed algorithm.     

The first constant factor approximation for minimum partial connected dominating set problem in growth-bounded graphs

The idea of virtual backbone has emerged to improve the efficiency of flooding based routing algorithms for wireless networks. The effectiveness of virtual backbone can be improved as its size decreases. The minimum connected dominating set (CDS) problem was used to compute minimum size virtual backbone. However, as this formulation requires the virtual backbone nodes to connect all other nodes, even the size of minimum virtual backbone can be large. This observation leads to consider the minimum partial CDS problem, whose goal is to compute a CDS serving only more than a certain portion of the nodes in a given network. So far, the performance ratio of the best approximation algorithm for the problem is \(O(\ln \varDelta ),\) where \(\varDelta\) is the maximum degree of the input general graph. In this paper, we first assume the input graph is a growth-bounded graph and introduce the first constant factor approximation for the problem. Later, we show that our algorithm is an approximation for the problem in unit disk graph with a much smaller performance ratio, which is of practical interest since unit disk graph is popular to abstract homogeneous wireless networks. Finally, we conduct simulations to evaluate the average performance of our algorithm.     

Approximation Algorithms for the Connected Dominating Set Problem in Unit Disk Graphs

The connected dominating set （CDS） problem, which consists of finding a smallest connected dominating set for graphs is an NP-hard problem in the unit disk graphs （UDGs）. This paper focuses on the CDS problem in wireless networks. Investigation of some properties of independent set （IS） in UDGs shows that geometric features of nodes distribution like angle and area can be used to design efficient heuristics for the approximation algorithms. Several constant factor approximation algorithms are presented for the CDS problem in UDGs. Simulation results show that the proposed algorithms perform better than some known ones.     

On Construction of Virtual Backbone in Wireless Ad Hoc Networks with Unidirectional Links

Since there is no fixed infrastructure in wireless ad hoc networks , virtual backbone has been proposed as the routing infrastructure to alleviate the broadcasting storm problem. The virtual backbone construction has been studied extensively in {em undirected} graphs, especially in unit disk graphs, in which each node has the same transmission range. In practice, however, transmission ranges of all nodes are not necessarily equal. In this paper, we model such a network as a disk graph, where unidirectional links are considered. To study the virtual backbone construction in disk graphs, we consider two problems: Strongly Connected Dominating Set (SCDS) and Strongly Connected Dominating and Absorbing Set (SCDAS). We propose a constant approximation algorithm and discuss its improvements for the SCDS problem . We also propose a heuristic for the SCDAS problem. Through extensive simulations, we verify our theoretical analysis and also demonstrate that the SCDS can be extended to form an SCDAS with marginal extra overhead.     

Construction and maintenance of virtual backbone in wireless networks

In ad hoc wireless networks, there is no predefined infrastructure and nodes communicate with each other via peer communications. In order to make routing efficient in such networks the connected dominating set (CDS) can act as virtual backbone for the network. A smaller virtual backbone suffers less from the interference problem and incurs less maintenance overhead. Computing minimum CDS backbone is proven to be NP-Hard, it is therefore desirable to use efficient heuristic algorithms to find a virtual backbone of small size. Diameter and average backbone path length (ABPL) are other major criteria for evaluation of the backbone produced by an algorithm. In this paper, after giving a brief survey of classical CDS algorithms, two new centralized algorithms are described for the construction of the virtual backbone and their performance has been compared with five recent algorithms (two centralized and three distributed) along the parameters: size, diameter, and ABPL. The new algorithms perform better on most of the criteria. The re-construction of entire CDS upon movement or failure of a few nodes is very costly in terms of processing power, battery utilization, bandwidth utilization etc., as compared to maintaining the CDS for the affected nodes, since the re-construction of the CDS is to be performed for the whole network while maintenance involves the affected nodes and their neighbours only. A new distributed algorithm is described that maintains the virtual backbone on movement or failure of a single node. The overhead of CDS maintenance with this algorithm compares very favourably against that of re-construction.     

基于极大独立集的最小连通支配集的分布式算法

全网范围的广播在无线传感器网络和移动自组织网络中有着广泛的应用.为节省网络资源,减少冗余转发节点成为广播中需解决的关键问题.广播过程中最小化参与转发节点数问题与图论中求解最小连通支配集问题等价,而在任意图中求解最小连通支配集是NP完全问题.本文基于极大独立集,提出了一种求解最小连通支配集的分布式算法(MISB),并证明了算法的正确性.仿真结果表明,使用该算法能得到较小的连通支配集,从而有效减少网络广播过程中的转发节点数,大大节省了网络资源.     

Rotation of CDS via Connected Domatic Partition in Ad Hoc Sensor Networks

Wireless ad hoc and sensor networks (WSNs) often require a connected dominating set (CDS) as the underlying virtual backbone for efficient routing. Nodes in a CDS have extra computation and communication load for their role as dominator, subjecting them to an early exhaustion of their battery. A simple mechanism to address this problem is to switch from one CDS to another fresh CDS, rotating the active CDS through a disjoint set of CDSs. This gives rise to the connected domatic partition (CDP) problem, which essentially involves partitioning the nodes V(G) of a graph G into node disjoint CDSs. We have developed a distributed algorithm for constructing the CDP using our maximal independent set (MIS)-based proximity heuristics, which depends only on connectivity information and does not rely on geographic or geometric information. We show that the size of a CDP that is identified by our algorithm is at least lfloor{frac{delta+1}{beta(c+1)}}rfloor-f, where delta is the minimum node degree of G, betaleq 2, cleq 11 is a constant for a unit disk graph (UDG), and the expected value of f is epsilondelta|V|, where epsilon ll 1 is a positive constant, and delta geq 48. Results of varied testing of our algorithm are positive even for a network of a large number of sensor nodes. Our scheme also performs better than other related techniques such as the ID-based scheme.     

A new distributed approximation algorithm for constructing minimum connected dominating set in wireless ad hoc networks

In recent years, constructing a virtual backbone by nodes in a connected dominating set (CDS) has been proposed to improve the performance of ad hoc wireless networks. In general, a dominating set satisfies that every vertex in the graph is either in the set or adjacent to a vertex in the set. A CDS is a dominating set that also induces a connected sub‐graph. However, finding the minimum connected dominating set (MCDS) is a well‐known NP‐hard problem in graph theory. Approximation algorithms for MCDS have been proposed in the literature. Most of these algorithms suffer from a poor approximation ratio, and from high time complexity and message complexity. In this paper, we present a new distributed approximation algorithm that constructs a MCDS for wireless ad hoc networks based on a maximal independent set (MIS). Our algorithm, which is fully localized, has a constant approximation ratio, and O(n) time and O(n) message complexity. In this algorithm, each node only requires the knowledge of its one‐hop neighbours and there is only one shortest path connecting two dominators that are at most three hops away. We not only give theoretical performance analysis for our algorithm, but also conduct extensive simulation to compare our algorithm with other algorithms in the literature. Simulation results and theoretical analysis show that our algorithm has better efficiency and performance than others. Copyright © 2005 John Wiley & Sons, Ltd.     

Efficient Topology Control for Ad-Hoc Wireless Networks with Non-Uniform Transmission Ranges

Wireless network topology control has drawn considerable attention recently. Priori arts assumed that the wireless ad hoc networks are modeled by unit disk graphs (UDG), i.e., two mobile hosts can communicate as long as their Euclidean distance is no more than a threshold. However, practically, the networks are never so perfect as unit disk graphs: the transmission ranges may vary due to various reasons such as the device differences, the network control necessity, and the perturbation of the transmission ranges even the transmission ranges are set as the same originally. Thus, we assume that each mobile host has its own transmission range. The networks are modeled by mutual inclusion graphs (MG), where two nodes are connected iff they are within the transmission range of each other. Previously, no method is known for topology control when the networks are modeled as mutual inclusion graphs.The paper proposes the first distributed mechanism to build a sparse power efficient network topology for ad hoc wireless networks with non-uniform transmission ranges. We first extend the Yao structure to build a spanner with a constant length and power stretch factor for mutual inclusion graph. We then propose two efficient localized algorithms to construct connected sparse network topologies. The first structure, called extended Yao-Yao, has node degree at most O(log ), where = max_u max_uvMG . The second structure, called extended Yao and Sink, has node degree bounded by O(log ), and is a length and power spanner. The methods are based on a novel partition strategy of the space surrounded each mobile host. Both algorithms have communication cost O(n) under a local broadcasting communication model, where each message has O(log n) bits.Xiang-Yang Li has been an Assistant Professor of Computer Science at the Illinois Institute of Technology since 2000. He received MS (2000) and PhD (2001) degree at Department of Computer Science from University of Illinois at Urbana-Champaign. He received his Bachelor degree at Department of Computer Science and Bachelor degree at Department of Business Management from Tsinghua University, P.R. China in 1995. His research interests span the computational geometry, wireless ad hoc networks, game theory, cryptography and network security. Recently, he focuses on performing research on the cooperation, energy efficiency, and distributed algorithms for wireless ad hoc and sensor networks. He served various positions at a number of international conferences. He recently co-organized a special issue of ACM MONET on non-cooperative computing in wireless networks. He is a member of the ACM, IEEE.Wen-Zhan Song received the B.S. degree and M.Eng. degree in computer science from Nanjing University of Science and Technology, Nanjing, in 1997 and 2000. He joined the Department of Computer Science, Illinois Institute of Technology as a Ph.D candidate in 2001. His research interests include wireless networks, and Peer-to-Peer systems.Yu Wang received the PhD degree in computer science from Illinois Institute of Technology in 2004, the BEng degree and the MEng degree in computer science from Tsinghua University, China, in 1998 and 2000. He has been an assistant professor of computer science at the Univeristy of North Carolina at Charlotte since 2004. His current research interests include wireless networks, mobile computing, algorithm design, and artificial intelligence. He is a member of the ACM, IEEE, and IEEE Communication Society.     

The Maximum Throughput of A Wireless Multi-Hop Path

In this paper, the maximum end-to-end throughput that can be achieved on a wireless multi-hop path is investigated analytically. The problem is modeled using the conflict graph, where each link in the multi-hop path is represented uniquely by a vertex in the conflict graph and two vertices are adjacent if and only if the associated links mutually interfere. Using the conflict graph and the linear programming formulations of the problem, we analyzed the maximum end-to-end throughput of a wireless multi-hop path a) in a simple scenario where nodes are optimally placed and each node can only interfere with the transmission of its adjacent nodes along the path, and b) in a more complicated scenario where nodes are randomly placed and each node can interfere with the transmission of any number of nearby nodes along the path in both a) an error free radio environment and b) an erroneous radio environment. The maximum end-to-end throughputs for each of the above four scenarios are obtained analytically. We show that the maximum achievable end-to-end throughput is determined by the throughput of its bottleneck clique, where a clique is a maximal set of mutually adjacent vertices in the associated conflict graph. Further our analysis suggests the optimum scheduling algorithm that can be used to achieve the maximum end-to-end throughput and that it is convenient to use the (maximal) independent sets as the basic blocks for the design of scheduling algorithms. The findings in this paper lay guidelines for the design of optimum scheduling algorithms. They can be used to design computationally efficient algorithms to determine the maximum throughput of a wireless multi-hop path and to design a scheduling algorithm to achieve that throughput.     

Robust position-based routing for wireless ad hoc networks

We consider a wireless ad hoc network composed of a set of wireless nodes distributed in a two dimensional plane. Several routing protocols based on the positions of the mobile hosts have been proposed in the literature. A typical assumption in these protocols is that all wireless nodes have uniform transmission regions modeled by unit disk centered at each wireless node. However, all these protocols are likely to fail if the transmission ranges of the mobile hosts vary due to natural or man-made obstacles or weather conditions. These protocols may fail because either some connections that are used by routing protocols do not exist, which effectively results in disconnecting the network, or the use of some connections causes livelocks. In this paper, we describe a robust routing protocol that tolerates up to roughly 40% of variation in the transmission ranges of the mobile hosts. More precisely, our protocol guarantees message delivery in a connected ad hoc network whenever the ratio of the maximum transmission range to the minimum transmission range is at most .     

Power Efficient Range Assignment for Symmetric Connectivity in Static Ad Hoc Wireless Networks

In this paper we study the problem of assigning transmission ranges to the nodes of a static ad hoc wireless network so as to minimize the total power consumed under the constraint that enough power is provided to the nodes to ensure that the network is connected. We focus on the Min-Power Symmetric Connectivity problem, in which the bidirectional links established by the transmission ranges are required to form a connected graph. Implicit in previous work on transmission range assignment under asymmetric connectivity requirements is the proof that Min-Power Symmetric Connectivity is NP-hard and that the MST algorithm has a performance ratio of 2. In this paper we make the following contributions: (1) we show that the related Min-Power Symmetric Unicast problem can be solved efficiently by a shortest-path computation in an appropriately constructed auxiliary graph; (2) we give an exact branch and cut algorithm based on a new integer linear program formulation solving instances with up to 35–40 nodes in 1 hour; (3) we establish the similarity between Min-Power Symmetric Connectivity and the classic Steiner Tree problem in graphs, and use this similarity to give a polynomial-time approximation scheme with performance ratio approaching 5/3 as well as a more practical approximation algorithm with approximation factor 11/6; and (4) we give the results of a comprehensive experimental study comparing new and previously proposed heuristics with the above exact and approximation algorithms.     

时延和能耗均衡的强连通支配集构造算法

针对无线传感器网络中链路的非对称性,提出时延约束的强连通支配树(SDTT,strongly connected dominating tree with bounded transmission delay)问题,给出在有向图上构建传输时延和能量消耗均衡的强连通支配集的强连通支配树(SCDT,distributed strongly connected dominating tree)算法。首先在单位圆图(UDG)模型的基础上构建极大独立集(MIS),然后在具有双向权值的有向图上基于最小支撑树和最短路径树实现分布式SCDT算法,同时满足时延和能耗均衡的约束条件要求。理论算例分析和仿真结果表明提出的算法能有效地解决SDTT问题,构造联合约束的强连通支配集,形成时延和能耗均衡的虚拟骨干。     

Separability and topology control of quasi unit disk graphs

A deep understanding of the structural properties of wireless networks is critical for evaluating the performance of network protocols and improving their designs. Many protocols for wireless networks—routing, topology control, information storage/retrieval and numerous other applications—have been based on the idealized unit-disk graph (UDG) network model. The significant deviation of the UDG model from many real wireless networks is substantially limiting the applicability of such protocols. A more general network model, the quasi unit-disk graph (quasi-UDG) model, captures much better the characteristics of wireless networks. However, the understanding of the properties of general quasi-UDGs has been very limited, which is impeding the designs of key network protocols and algorithms. In this paper, we present results on two important properties of quasi-UDGs: separability and the existence of power efficient spanners. Network separability is a fundamental property leading to efficient network algorithms and fast parallel computation. We prove that every quasi-UDG has a corresponding grid graph with small balanced separators that captures its connectivity properties. We also study the problem of constructing an energy-efficient backbone for a quasi-UDG. We present a distributed local algorithm that, given a quasi-UDG, constructs a nearly planar backbone with a constant stretch factor and a bounded degree. We demonstrate the excellent performance of these auxiliary graphs through simulations and show their applications in efficient routing.     

Topology control in ad hoc wireless networks using cooperative communication

In this paper, we address the Topology control with Cooperative Communication (TCC) problem in ad hoc wireless networks. Cooperative communication is a novel model introduced recently that allows combining partial messages to decode a complete message. The objective of the TCC problem is to obtain a strongly-connected topology with minimum total energy consumption. We show that the TCC problem is NIP-complete and design two distributed and localized algorithms to be used by the nodes to set up their communication ranges. Both algorithms can be applied on top of any symmetric, strongly-connected topology to reduce total power consumption. The first algorithm uses a distributed decision process at each node that makes use of only 2-hop neighborhood information. The second algorithm sets up the transmission ranges of nodes iteratively, over a maximum of six steps, using only 1-hop neighborhood information. We analyze the performance of our approaches through extensive simulation.     

Achieving energy‐neutral data transmission by adjusting transmission power for energy‐harvesting wireless sensor networks

Recently, benefiting from rapid development of energy harvesting technologies, the research trend of wireless sensor networks has shifted from the battery‐powered network to the one that can harvest energy from ambient environments. In such networks, a proper use of harvested energy poses plenty of challenges caused by numerous influence factors and complex application environments. Although numerous works have been based on the energy status of sensor nodes, no work refers to the issue of minimizing the overall data transmission cost by adjusting transmission power of nodes in energy‐harvesting wireless sensor networks. In this paper, we consider the optimization problem of deriving the energy‐neutral minimum cost paths between the source nodes and the sink node. By introducing the concept of energy‐neutral operation, we first propose a polynomial‐time optimal algorithm for finding the optimal path from a single source to the sink by adjusting the transmission powers. Based on the work earlier, another polynomial‐time algorithm is further proposed for finding the approximated optimal paths from multiple sources to the sink node. Also, we analyze the network capacity and present a near‐optimal algorithm based on the Ford–Fulkerson algorithm for approaching the maximum flow in the given network. We have validated our algorithms by various numerical results in terms of path capacity, least energy of nodes, energy ratio, and path cost. Simulation results show that the proposed algorithms achieve significant performance enhancements over existing schemes. Copyright © 2016 John Wiley & Sons, Ltd.     

基于极大权的最小连通支配集启发式算法

Ad hoc无线网络中基于最小连通支配集(MCDS)的路由是一个引人瞩目的方法,文中提出了一种基于极大权的MCDS的启发式算法,确保了性能强的主机担任网关节点的角色,能更好的协调管理网络中其他的节点,从而保持MCDS的相对稳固性并为全网中的广播和路由操作提供一个高效的通信基础.仿真结果表明,该算法能在保证生成权和极大的连通支配集的同时也确保它的极小性,因此能有效地用于基于MCDS的路由设计中.     

Upper bounding service capacity in multi-hop wireless SSMA-based ad hoc networks

Upper bounds on the service carrying capacity of a multi-hop, wireless, SSMA-based ad hoc network are considered herein. The network has a single radio band for transmission and reception. Each node can transmit to, or receive from, multiple nodes simultaneously. We formulate the scheduling of transmissions and control of transmit powers as a joint, mixed-integer, nonlinear optimization problem that yields maximum return at minimum power subject to SINR constraints. We present an efficient tabu search-based heuristic algorithm to solve the optimization problem and rigorously assess the quality of the results. Through analysis and simulation, we establish upper bounds on the VoIP call carrying capacity of the network as function of various parameters. We discuss the pros and cons of using SSMA as a spectrum sharing technique in wireless ad hoc networks.     

Efficient broadcast for wireless ad hoc networks with a realistic physical layer

In this paper, we investigate the low coverage problem of efficient broadcast protocols in wireless ad hoc networks with realistic physical layer models. To minimize energy consumption, efficient protocols aim to select small set of forward nodes and minimum transmission radii. In ideal physical layer model, nodes within forward nodes’ transmission ranges can definitely receive packets; therefore energy efficient protocols can guarantee full coverage for broadcasting. However, in networks with a realistic physical layer, nodes can only receive packets with probability. We present an analytical model to show that the transmission radii used for nodes can be used to establish a tradeoff between minimizing energy consumption and ensuring network coverage. We then propose a mechanism called redundant radius, which involves using two transmission radii, to form a buffer zone that guarantees the availability of logical links in the physical network, one for broadcast tree calculation and the other for actual data transmission. With this mechanism, we extend well-known centralized protocols, BIP and DBIP, and corresponding localized protocols, LBIP and LDBIP. The effectiveness of the proposed scheme in improving network coverage is validated analytically and by simulation.     

Polynomial time solution to minimum forwarding set problem in wireless networks under disk coverage model

In this paper, we consider a practical problem, called Minimum Forwarding Set Problem (MFSP), that emerges within the context of implementing (energy efficient) communication protocols for wireless ad hoc or sensor networks. For a given node v, MFSP asks for a minimum cardinality subset of 1-hop neighbors of v to cover v’s 2-hop neighbors. MFSP problem is also known as multi-point relay (MPR) problem. It is shown to be an NP-complete problem for its general case that does not consider the coverage characteristics of wireless transmissions. In this paper, we present two polynomial time algorithms to solve the MFSP problem under disk coverage model for wireless transmissions. In our earlier work, we presented a polynomial time algorithm for this problem under unit disk coverage model. In the current work, we present several observations on the geometric characteristics of wireless transmissions under disk coverage model and build two alternative dynamic programming based solutions with different run time and space complexities to the problem. Disk coverage model is a more general model because it allows nodes to use arbitrary power levels for transmissions. As a result, the presented algorithms provide a more practical solution that can be used as a building block for energy efficient communication protocols designed for wireless ad hoc and sensor networks.