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41
An Aloha protocol for multihop mobile wireless networks
 IEEE Trans. Inf. Theory
, 2006
"... Abstract—An Alohatype access control mechanism for large mobile, multihop, wireless networks is defined and analyzed. This access scheme is designed for the multihop context, where it is important to find a compromise between the spatial density of communications and the range of each transmission. ..."
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Cited by 225 (24 self)
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Abstract—An Alohatype access control mechanism for large mobile, multihop, wireless networks is defined and analyzed. This access scheme is designed for the multihop context, where it is important to find a compromise between the spatial density of communications and the range of each transmission. More precisely, the analysis aims at optimizing the product of the number of simultaneously successful transmissions per unit of space (spatial reuse) by the average range of each transmission. The optimization is obtained via an averaging over all Poisson configurations for the location of interfering mobiles, where an exact evaluation of signal over noise ratio is possible. The main mathematical tools stem from stochastic geometry and are spatial versions of the socalled additive and max shot noise processes. The resulting medium access control (MAC) protocol exhibits some interesting properties. First, it can be implemented in a decentralized way provided some local geographic information is available to the mobiles. In addition, its transport capacity is proportional to the square root of the density of mobiles which is the upper bound of Gupta and Kumar. Finally, this protocol is selfadapting to the node density and it does not require prior knowledge of this density. Index Terms—Medium access control (MAC) layer, multipleaccess protocol, network design, optimization, point process, queuing theory, signaltointerference ratio, stochastic geometry, stochastic process, transport capacity. I.
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 84 (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.
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 76 (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.
Fault Tolerant Deployment and Topology Control in Wireless Networks
 In Proceedings of the Fourth ACM Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc
, 2003
"... This paper investigate fault tolerance for wireless ad hoc networks. We consider a largescale of wireless networks whose nodes are distributed randomly in a unitarea square region. Given n wireless nodes V , each with transmission range rn , the wireless networks are often modeled by graph G(V,rn ..."
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Cited by 70 (2 self)
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This paper investigate fault tolerance for wireless ad hoc networks. We consider a largescale of wireless networks whose nodes are distributed randomly in a unitarea square region. Given n wireless nodes V , each with transmission range rn , the wireless networks are often modeled by graph G(V,rn ) in which two nodes are connected if their Euclidean distance is no more than rn .
Network Lifetime and Power Assignment in AdHoc Wireless Networks
 IN ESA
, 2003
"... 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 subgra ..."
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Cited by 53 (4 self)
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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
A Statistical Analysis of the LongRun Node Spatial Distribution in Mobile Ad Hoc Networks
, 2002
"... In this paper, we analyze the node spatial distribution of a mobile wireless ad hoc networks. Characterizing this distribution is of fundamental importance in the analysis of many relevant properties of mobile ad hoc networks, such as connectivity, average route length, and network capacity. In part ..."
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Cited by 42 (5 self)
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In this paper, we analyze the node spatial distribution of a mobile wireless ad hoc networks. Characterizing this distribution is of fundamental importance in the analysis of many relevant properties of mobile ad hoc networks, such as connectivity, average route length, and network capacity. In particular, we have investigated under what conditions the node spatial distribution resulting after a large number of mobility steps resembles the uniform distribution. This is motivated by the fact that the existing theoretical results concerning mobile ad hoc networks are based on this assumption. In order to test this hypothesis, we performed extensive simulations using two wellknown mobility models: the random waypoint model, which resembles intentional movement, and a Brownianlike model, which resembles nonintentional movement. Our analysis has shown that in the Brownianlike motion the uniformity assumption does hold, and that the intensity of the concentration of nodes in the center of the deployment region that occurs in the random waypoint model heavily depends on the choice of some mobility parameters. For extreme values of these parameters, the uniformity assumption is impaired.
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 33 (10 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.
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 31 (2 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.
Minimumpower multicast routing in static ad hoc wireless networks
 IEEE/ACM Trans. Netw
, 2004
"... (broadcasting incremental power). Wan et al. (2001) proved that SPT has an approximation ratio of at least ( 2) where is the total number of nodes, and both MST and BIP have constant approximation ratios. Based on the approach of pruning, Wieselthier et al. also proposed three greedy heuristics for ..."
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Cited by 29 (0 self)
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(broadcasting incremental power). Wan et al. (2001) proved that SPT has an approximation ratio of at least ( 2) where is the total number of nodes, and both MST and BIP have constant approximation ratios. Based on the approach of pruning, Wieselthier et al. also proposed three greedy heuristics for MinPower Asymmetric Multicast Routing: PSPT (pruned shortestpath tree), PMST (pruned minimum spanning tree), and PBIP (pruned broadcasting incremental power). In this paper, we first prove that the approximation ratios of these three heuristics are at least ( 1 2) 1, and 2 (1), respectively. We then present constantapproxiation algorithms for MinPower Asymmetric Multicast Routing. We show that anyapproximation Steiner tree algorithm gives rise to aapproximation heuristic for MinPower Asymmetric Multicast Routing, where is a constant between 6 and 12. In particular, the TakahashiMatsuyama Steiner tree heuristic leads to a heuristic called SPF (shortestpath first), which has an approximation ratio of at most 2. We also present another heuristic, called MIPF (minimum incremental path first), for MinPower Asymmetric Multicast Routing and show that its approximation ratio is between (13 3) and 2. Both SPF and MIPF can be regarded as an adaptation of MST and BIP, respectively, in a different manner than pruning. Finally, we prove that anyapproximation Steiner tree algorithm also gives rise to a 2approximation algorithm for MinPower Symmetric Multicast Routing. Index Terms—Approximation algorithms, multicast routing, power control. I.
Power efficient range assignment in adhoc wireless networks
 IN PROC. IEEE WIRELESS COMMUNICATIONS AND NETWORKING CONFERENCE (WCNC
, 2003
"... 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 354 ..."
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Cited by 26 (2 self)
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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.