Topology control algorithms allow each node in a wireless multi-hop network to adjust the power at which it makes its transmissions and choose the set of neighbors with which it communicates directly, while preserving global goals such as connectivity or coverage. This allows each node to conserve energy and contribute to increasing the lifetime of the network. In this paper, in contrast to most previous work, we consider (i) both the energy costs of communication as well as the amount of available energy at each node, (ii) the realistic situation of varying rates of energy consumption at different nodes, and (iii) the fact that co-operation between nodes, where some nodes make a sacrifice by increasing energy consumption to help other nodes reduce their consumption, can be used to extend network lifetime. This paper introduces a new distributed topology control algorithm, called the Cooperative Topology Control with Adaptation (CTCA), based on a game-theoretic approach that maps the problem of maximizing the network's lifetime into an ordinal potential game. We prove the existence of a Nash equilibrium for the game. Our simulation results indicate that the CTCA algorithm extends the life of a network by more than 50 compared to the best previously-known algorithm. We also study the performance of the distributed CTCA algorithm in comparison to an optimal centralized algorithm as a function of the communication ranges of nodes and node density.
Traditional topology control algorithms such as Small Minimum-Energy Communication Network (SMECN) @cite_9 , Minimum Spanning Tree (MST) @cite_27 , DRNG @cite_35 , DLSS @cite_35 and STC @cite_25 usually start the topology control process with each node transmitting at its maximum transmission power to discover all of its neighbors. Local neighborhood and power-level information is next exchanged between neighbors. The minimum transmission power of each node such that the graph is still connected is later computed at each node without further communication between nodes. The Weighted Dynamic Topology Control (WDTC) @cite_3 algorithm improves upon the work of MST, and considers the remaining energy of each node in addition to the energy cost of communication across each pair of nodes. The algorithm, however, forces bidirectional communication between each pair of nodes and, in addition, requires periodic communication by each node at its maximum possible power level. Other related algorithms seek to offer a robust topology where the graph can stand multiple channel failures; for example, a @math -connected graph is sought in @cite_19 @cite_6 and a two-tiered network in @cite_26 .
@cite_35 @cite_26 @cite_9 @cite_3 @cite_6 @cite_19 @cite_27 @cite_25
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Most existing topology control algorithms assume homogeneous wireless networks with uniform maximal transmission power, and cannot be directly applied to heterogeneous wireless networks where the maximal transmission power of each node may be different. We present two localized topology control algorithms for heterogeneous networks: Directed Relative Neighborhood Graph (DRNG) and Directed Local Spanning Subgraph (DLSS). In both algorithms, each node independently builds its neighbor set by adjusting the transmission power, and defines the network topology by using only local information. We prove that: 1) both DRNG and DLSS can preserve network connectivity; 2) the out-degree of any node in the resulting topology generated by DRNG or DLSS is bounded by a constant; and 3) DRNG and DLSS can preserve network bi-directionality. Simulation results indicate that DRNG and DLSS significantly outperform existing topology control algorithms for heterogeneous networks in several aspects. We consider a two-tiered Wireless Sensor Network (WSN) consisting of sensor clusters deployed around strategic locations and base-stations (BSs) whose locations are relatively flexible. Within a sensor cluster, there are many small sensor nodes (SNs) that capture, encode and transmit relevant information from the designated area, and there is at least one application node (AN) that receives raw data from these SNs, creates a comprehensive local-view, and forwards the composite bit-stream toward a BS. In practice, both SN and AN are battery-powered and energy-constrained, and their node lifetimes directly affect the network lifetime of WSNs. In this paper, we focus on the topology control process for ANs and BSs, which constitute the upper tier of a two-tiered WSN. We propose approaches to maximize the topological network lifetime of the WSN, by arranging BS location and inter-AN relaying optimally. Based on an algorithm in Computational Geometry, we derive the optimal BS locations under three topological lifetime definitions according to mission criticality. In addition, by studying the intrinsic properties of WSNs, we establish the upper and lower bounds of their maximal topological lifetime. When inter-AN relaying becomes feasible and favorable, we continue to develop an optimal parallel relay allocation to further prolong the topological lifetime of the WSN. An equivalent serialized relay schedule is also obtained, so that each AN only needs to have one relay destination at any time throughout the mission. The experimental performance evaluation demonstrates the efficacy of topology control as a vital process to maximize the network lifetime of WSNs. We propose a protocol that, given a communication network, computes a subnetwork such that, for every pair @math of nodes connected in the original network, there is a minimum-energy path between @math and @math in the subnetwork (where a minimum-energy path is one that allows messages to be transmitted with a minimum use of energy). The network computed by our protocol is in general a subnetwork of the one computed by the protocol given in [13]. Moreover, our protocol is computationally simpler. We demonstrate the performance improvements obtained by using the subnetwork computed by our protocol through simulation. In this paper a new energy-aware weighted dynamic topology control (WDTC) algorithm is proposed to extend the lifetime of wireless network and balance the nodes’ energy consumption. The idea is that each node builds its local minimum spanning tree (MST) based on the energy-aware weighted graph and the network topology is adjusted accordingly. It was proved theoretically that the topology under WDTC algorithm could preserve the network connectivity and a sufficient condition for the degree of no more than 6 was also given. Simulation shows that WDTC algorithm can effectively prolong the network lifetime and has good topological features. In ad hoc wireless networks, it is crucial to minimize power consumption while maintaining key network properties. This work studies power assignments of wireless devices that minimize power while maintaining k-fault tolerance. Specifically, we require all links established by this power setting be symmetric and form a k-vertex connected subgraph of the network graph. This problem is known to be NP-hard. We show current heuristic approaches can use arbitrarily more power than the optimal solution. Hence, we seek approximation algorithms for this problem. We present three approximation algorithms. The first algorithm gives an O(kalpha)-approximation where is the best approximation factor for the related problem in wired networks (the best alpha so far is O(log k)). With a more careful analysis, we show our second (slightly more complicated) algorithm is an O(k)-approximation. Our third algorithm assumes that the edge lengths of the network graph form a metric. In this case, we present simple and practical distributed algorithms for the cases of 2- and 3-connectivity with constant approximation factors. We generalize this algorithm to obtain an O(k2c+2)-approximation for general k-connectivity (2 les c les 4 is the power attenuation exponent). Finally, we show that these approximation algorithms compare favorably with existing heuristics. We note that all algorithms presented in this paper can be used to minimize power while maintaining -edge connectivity with guaranteed approximation factors. Recently, different set of authors used the notion of k-connectivity and the results of this paper to deal with the fault-tolerance issues for static wireless network settings. In this paper, we present a minimum spanning tree (MST) based topology control algorithm, called local minimum spanning tree (LMST), for wireless multi-hop networks. In this algorithm, each node builds its local minimum spanning tree independently and only keeps on-tree nodes that are one-hop away as its neighbors in the final topology. We analytically prove several important properties of LMST: (1) the topology derived under LMST preserves the network connectivity; (2) the node degree of any node in the resulting topology is bounded by 6; and (3) the topology can be transformed into one with bidirectional links (without impairing the network connectivity) after removal of all uni-directional links. These results are corroborated in the simulation study. Each node in a wireless multi-hop network can adjust the power level at which it transmits and thus change the topology of the network to save energy by choosing the neighbors with which it directly communicates. Many previous algorithms for distributed topology control have assumed an ability at each node to deduce some location-based information such as the direction and the distance of its neighbor nodes with respect to itself. Such a deduction of location-based information, however, cannot be relied upon in real environments where the path loss exponents vary greatly leading to significant errors in distance estimates. Also, multipath effects may result in different signal paths with different loss characteristics, and none of these paths may be line-of-sight, making it difficult to estimate the direction of a neighboring node. In this paper, we present Step Topology Control (STC), a simple distributed topology control algorithm which reduces energy consumption while preserving the connectivity of a heterogeneous sensor network without use of any location-based information. The STC algorithm avoids the use of GPS devices and also makes no assumptions about the distance and direction between neighboring nodes. We show that the STC algorithm achieves the same or better order of communication and computational complexity when compared to other known algorithms that also preserve connectivity without the use of location-based information. We also present a detailed simulation-based comparative analysis of the energy savings and interference reduction achieved by the algorithms. The results show that, in spite of not incurring a higher communication or computational complexity, the STC algorithm performs better than other algorithms in uniform wireless environments and especially better when path loss characteristics are non-uniform.