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46
The Critical Transmitting Range for Connectivity in Sparse Wireless Ad Hoc Networks
, 2003
"... In this paper, we analyze the critical transmitting range for connectivity in wireless ad hoc networks. More specifically, we consider the following problem: assume n nodes, each capable of communicating with nodes within a radius of r, are randomly and uniformly distributed in a ddimensional re ..."
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Cited by 106 (12 self)
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In this paper, we analyze the critical transmitting range for connectivity in wireless ad hoc networks. More specifically, we consider the following problem: assume n nodes, each capable of communicating with nodes within a radius of r, are randomly and uniformly distributed in a ddimensional region with a side of length l; how large must the transmitting range r be to ensure that the resulting network is connected with high probability? First, we consider this problem for stationary networks, and we provide tight upper and lower bounds on the critical transmitting range for onedimensional networks, and nontight bounds for two and threedimensional networks. Due to the presence of the geometric parameter l in the model, our results can be applied to dense as well as sparse ad hoc networks, contrary to existing theoretical results that apply only to dense networks. We also investigate several related questions through extensive simulations. First, we evaluate the relationship between the critical transmitting range and the minimum transmitting range that ensures formation of a connected component containing a large fraction (e.g. 90%) of the nodes. Then, we consider the mobile version of the
Power Optimization in FaultTolerant Topology Control Algorithms for Wireless Multihop Networks
 in Proceedings of the 9th Annual International Conference on Mobile Computing and Networking. 2003
, 2003
"... 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 kfault tolerance. Specifically, we require all links established by this power setting be ..."
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Cited by 56 (6 self)
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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 kfault tolerance. Specifically, we require all links established by this power setting be symmetric and form a kvertex connected subgraph of the network graph. This problem is known to be NPhard. 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(kα)approximation where α is the best approximation factor for the related problem in wired networks (the best α 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 3connectivity with constant approximation factors. We generalize this algorithm to obtain an O(k 2c+2)approximation for general kconnectivity (2 ≤ c ≤ 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 kedge connectivity with guaranteed approximation factors.
Minimum energy disjoint path routing in wireless adhoc networks
 in Proceedings of the 9th Annual International Conference on Mobile Computing and Networking
, 2003
"... We develop algorithms for finding minimum energy disjoint paths in an allwireless network, for both the node and linkdisjoint cases. Our major results include a novel polynomial time algorithm that optimally solves the minimum energy 2 linkdisjoint paths problem, as well as a polynomial time algor ..."
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Cited by 47 (1 self)
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We develop algorithms for finding minimum energy disjoint paths in an allwireless network, for both the node and linkdisjoint cases. Our major results include a novel polynomial time algorithm that optimally solves the minimum energy 2 linkdisjoint paths problem, as well as a polynomial time algorithm for the minimum energy k nodedisjoint paths problem. In addition, we present efficient heuristic algorithms for both problems. Our results show that linkdisjoint paths consume substantially less energy than nodedisjoint paths. We also found that the incremental energy of additional linkdisjoint paths is decreasing. This finding is somewhat surprising due to the fact that in general networks additional paths are typically longer than the shortest path. However, in a wireless network, additional paths can be obtained at lower energy due to the broadcast nature of the wireless medium. Finally, we discuss issues regarding distributed implementation and present distributed versions of the optimal centralized algorithms presented in the paper.
Deploying Sensor Networks with Guaranteed Fault Tolerance
, 2005
"... We consider the problem of deploying or repairing a sensor network to guarantee a specified level of multipath connectivity (kconnectivity) between all nodes. Such a guarantee simultaneously provides fault tolerance against node failures and high overall network capacity (by the maxflow mincut t ..."
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Cited by 44 (4 self)
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We consider the problem of deploying or repairing a sensor network to guarantee a specified level of multipath connectivity (kconnectivity) between all nodes. Such a guarantee simultaneously provides fault tolerance against node failures and high overall network capacity (by the maxflow mincut theorem). We design and analyze the first algorithms that place an almostminimum number of additional sensors to augment an existing network into a kconnected network, for any desired parameter k. Our algorithms have provable guarantees on the quality of the solution. Specifically, we prove that the number of additional sensors is within a constant factor of the absolute minimum, for any fixed k. We have implemented greedy and distributed versions of this algorithm, and demonstrate in simulation that they produce highquality placements for the additional sensors.
Network Lifetime and Power Assignment in AdHoc Wireless Networks
 in ESA
, 2003
"... Abstract. Used for topology control in adhoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity) The input consists of a directed complete weighted graph G = (V; c). The power of a vertex u in a directed spanni ..."
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Cited by 43 (3 self)
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Abstract. Used for topology control in adhoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity) The input consists of a directed complete weighted graph G = (V; c). The power of a vertex u in a directed spanning subgraph H is given by pH(u) = maxuv2E(H) c(uv). The power of H is given by p(H) = P u2V pH(u), Power Assignment seeks to minimize p(H) while H satisfies the given connectivity constraint. We
On The Symmetric Range Assignment Problem In Wireless Ad Hoc Networks
, 2002
"... In this paper we consider a constrained version of the range assignment problem for wireless ad hoc networks, where the value the node transmitting ranges must be assigned in such a way that the resulting communication graph is strongly connected and the energy cost is minimum. We impose the further ..."
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Cited by 37 (1 self)
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In this paper we consider a constrained version of the range assignment problem for wireless ad hoc networks, where the value the node transmitting ranges must be assigned in such a way that the resulting communication graph is strongly connected and the energy cost is minimum. We impose the further requirement of symmetry on the resulting communication graph. We also consider a weaker notion of symmetry, in which only the existence of a set of symmetric edges that renders the communication graph connected is required. Our interest in these problems is motivated by the fact that a (weakly) symmetric range assignment can be more easily integrated with existing higher and lowerlevel protocols for ad hoc networks, which assume that all the nodes have the same transmitting range. We show that imposing symmetry does not change the complexity of the problem, which remains NPhard in two and threedimensional networks. We also show that a weakly symmetric range assignment can reduce the energy cost considerably with respect to the homogeneous case, in which all the nodes have the same transmitting range, and that no further (asymptotic) bene t is expected from the asymmetric range assignment. Hence, the results presented in this paper indicate that weak symmetry is a desirable property of the range assignment.
Some Recent Theoretical Advances and Open Questions on Energy Consumption in AdHoc Wireless Networks
, 2002
"... One of the main benefits of power controlled adhoc wireless networks is their ability to vary the range in order to reduce the power consumption. Minimizing energy consumption is crucial on such kind of networks since, typically, wireless devices are portable and benefit only of limited power resou ..."
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Cited by 29 (9 self)
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One of the main benefits of power controlled adhoc wireless networks is their ability to vary the range in order to reduce the power consumption. Minimizing energy consumption is crucial on such kind of networks since, typically, wireless devices are portable and benefit only of limited power resources. On the other hand, the network must have a sufficient degree of connectivity in order to guarantee fast and efficient communication. These two aspects yield a class of fundamental optimization problems, denoted as range assignment problems, that have been the subject of several works in the area of wireless network theory. The primary aim of this paper is to describe the most important recent advances on this class of problems. Rather than completeness, the paper will try to provide results and techniques that seem to be the most promising to address the several important related problems which are still open. Discussing such related open problems are indeed our other main goal.
Algorithmic, Geometric and Graphs Issues in Wireless Networks
 Wireless Communications and Mobile Computing
, 2002
"... We present an overview of the recent progress of applying computational geometry techniques to solve some questions, such as topology construction and broadcasting, in wireless ad hoc networks. Treating each wireless device as a node in a two dimensional plane, we model the wireless networks by unit ..."
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Cited by 25 (2 self)
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We present an overview of the recent progress of applying computational geometry techniques to solve some questions, such as topology construction and broadcasting, in wireless ad hoc networks. Treating each wireless device as a node in a two dimensional plane, we model the wireless networks by unit disk graphs in which two nodes are connected if their Euclidean distance is no more than one. We rst summarize the current status of constructing sparse spanners for unit disk graphs with various combinations of the following properties: bounded stretch factor, bounded node degree, planar, and bounded total edges weight (compared with the minimum spanning tree). Instead of constructing subgraphs by removing links, we then review the algorithms for constructing a sparse backbone (connected dominating set), i.e., subgraph from the subset of nodes. We then review some ecient methods for broadcasting and multicasting with theoretic guaranteed performance.
Power efficient range assignment for symmetric connectivity in static adhoc wireless networks
 WIRELESS NETWORKS
, 2006
"... 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 MINPOWER SYMMETRIC ..."
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Cited by 19 (1 self)
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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 MINPOWER 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 MINPOWER SYMMETRIC CONNECTIVITY is NPhard and that the MST algorithm has an approximation ratio of 2. In this paper we make the following contributions: (1) we show that the related MINPOWER SYMMETRIC UNICAST problem can be solved efficiently by a shortestpath computation in an appropriately constructed graph. (2) we give an exact branch and cut algorithm based on a new integer linear program formulation solving instances with up to 3540 nodes in 1 hour; (3) we establish the similarity between MINPOWER SYMMETRIC CONNECTIVITY and the classic STEINER TREE problem in graphs, and use this similarity to give a polynomialtime 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 a comprehensive experimental study comparing new and previously proposed heuristics with the above exact and approximation algorithms.
Power efficient range assignment in adhoc wireless networks
 In Proc. IEEE Wireless Communications and Networking Conference (WCNC
, 2003
"... Abstract—We study the problem of assigning transmission ranges to the nodes of ad hoc wireless networks so that to minimize power consumption while ensuring network connectivity. We give (1) an exact branch and cut algorithm based on a new integer linear program formulation solving instances with up ..."
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Cited by 19 (2 self)
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Abstract—We study the problem of assigning transmission ranges to the nodes of ad hoc wireless networks so that to minimize power consumption while ensuring network connectivity. We give (1) an exact branch and cut algorithm based on a new integer linear program formulation solving instances with up to 3540 nodes in 1 hour; (2) a proof that MINPOWER SYMMETRIC CONNECTIVITY WITH ASYMMETRIC POWER REQUIREMENTS is inapproximable within £¥¤§¦©¨������� � �� � factor for ¨��� � any unless; (3) an improved analysis for two approximation algorithms recently proposed by Călinescu et al. (TCS’02), decreasing the best known approximation factor to �������� ¨ ; (4) a comprehensive experimental study comparing new and previously proposed heuristics with the above exact and approximation algorithms.