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Maximizing Capacity in Arbitrary Wireless Networks in the SINR Model: Complexity and Game Theory
"... Abstract—In this paper we consider the problem of maximizing the number of supported connections in arbitrary wireless networks where a transmission is supported if and only if the signaltointerferenceplusnoise ratio at the receiver is greater than some threshold. The aim is to choose transmissi ..."
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Cited by 53 (3 self)
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Abstract—In this paper we consider the problem of maximizing the number of supported connections in arbitrary wireless networks where a transmission is supported if and only if the signaltointerferenceplusnoise ratio at the receiver is greater than some threshold. The aim is to choose transmission powers for each connection so as to maximize the number of connections for which this threshold is met. We believe that analyzing this problem is important both in its own right and also because it arises as a subproblem in many other areas of wireless networking. We study both the complexity of the problem and also present some game theoretic results regarding capacity that is achieved by completely distributed algorithms. We also feel that this problem is intriguing since it involves both continuous aspects (i.e. choosing the transmission powers) as well as discrete aspects (i.e. which connections should be supported).
A ConstantFactor Approximation for Wireless Capacity Maximization with Power Control in the SINR Model
 In Proc. of the 22nd annual ACMSIAM symposium on Discrete algorithms (SODA
, 2011
"... In modern wireless networks devices are able to set the power for each transmission carried out. Experimental but also theoretical results indicate that such power control can improve the network capacity significantly. We study this problem in the physical interference model using SINR constraints. ..."
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Cited by 50 (9 self)
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In modern wireless networks devices are able to set the power for each transmission carried out. Experimental but also theoretical results indicate that such power control can improve the network capacity significantly. We study this problem in the physical interference model using SINR constraints. In the SINR capacity maximization problem, we are given n pairs of senders and receivers, located in a metric space (usually a socalled fading metric). The algorithm shall select a subset of these pairs and choose a power level for each of them with the objective of maximizing the number of simultaneous communications. This is, the selected pairs have to satisfy the SINR constraints with respect to the chosen powers. We present the first algorithm achieving a constantfactor approximation in fading metrics. The best previous results depend on further network parameters such as the ratio of the maximum and the minimum distance between a sender and its receiver. Expressed only in terms of n, they are (trivial) Ω(n) approximations. Our algorithm still achieves an O(log n) approximation if we only assume to have a general metric space rather than a fading metric. Furthermore, existing approaches work well together with the algorithm allowing it to be used in singlehop and multihop scheduling scenarios. Here, we also get polylog n approximations. 1
Wireless scheduling with power control
 In Proc. 17th European Symposium on Algorithms (ESA
, 2009
"... We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that e ..."
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Cited by 43 (6 self)
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We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that each set satisfies the signaltointerferenceplusnoise (SINR) constraints. We give an algorithm that attains an approximation ratio of O(log n · log log Λ), where Λ is the ratio between the longest and the shortest linklength. Under the natural assumption that lengths are represented in binary, this gives the first polylog(n)approximation. The algorithm has the desirable property of using an oblivious power assignment, where the power assigned to a sender depends only on the length of the link. We show this dependence on Λ to be unavoidable, giving a construction for which any oblivious power assignment results in a Ω(log log Λ)approximation. We also give a simple online algorithm that yields a O(log Λ)approximation, by a reduction to the coloring of unitdisc graphs. In addition, we obtain improved approximation for a bidirectional variant of the scheduling problem, give partial answers to questions about the utility of graphs for modeling physical interference, and generalize the setting from the standard 2dimensional Euclidean plane to doubling metrics. 1
CMAC: Modeldriven Concurrent Medium Access Control for Wireless Sensor Networks
"... This paper presents CMAC, a new MAC protocol designed to achieve highthroughput bulk communication for dataintensive sensing applications. CMAC exploits concurrent wireless channel access based on empirical power control and physical interference models. Nodes running CMAC estimate the level of ..."
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Cited by 39 (11 self)
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This paper presents CMAC, a new MAC protocol designed to achieve highthroughput bulk communication for dataintensive sensing applications. CMAC exploits concurrent wireless channel access based on empirical power control and physical interference models. Nodes running CMAC estimate the level of interference based on the physical SignaltoInterferenceplusNoiseRatio (SINR) model and adjust the transmission power accordingly for concurrent channel access. CMAC employs a blockbased communication mode that not only amortizes the overhead of channel assessment, but also improves the probability that multiple nodes within the interference range of each other can transmit concurrently. CMAC has been implemented in TinyOS1.x and extensively evaluated on Tmote nodes. Our experiments show that CMAC significantly outperforms the stateofart CSMA protocol in TinyOS with respect to system throughput, delay and energy consumption.
Distributed contention resolution in wireless networks
 In DISC
, 2010
"... We present and analyze simple distributed contention resolution protocols for wireless networks. In our setting, one is given n pairs of senders and receivers located in a metric space. Each sender wants to transmit a signal to its receiver at a prespecified power level, e. g., all senders use the s ..."
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Cited by 36 (5 self)
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We present and analyze simple distributed contention resolution protocols for wireless networks. In our setting, one is given n pairs of senders and receivers located in a metric space. Each sender wants to transmit a signal to its receiver at a prespecified power level, e. g., all senders use the same, uniform power level as it is typically implemented in practice. Our analysis is based on the physical model in which the success of a transmission depends on the SignaltoInterferenceplusNoiseRatio (SINR). The objective is to minimize the number of time slots until all signals are successfully transmitted. Our main technical contribution is the introduction of a measure called maximum average affectance enabling us to analyze random contentionresolution algorithms in which each packet is transmitted in each step with a fixed probability depending on the maximum average affectance. We prove that the schedule generated this way is only an O(log 2 n) factor longer than the optimal one, provided that the prespecified power levels satisfy natural monontonicity properties. By modifying the algorithm, senders need not to know the maximum average affectance in advance but only static information about the network. In addition, we extend our approach to multihop communication achieving the same appoximation factor.
A fast distributed approximation algorithm for minimum spanning trees
 IN PROCEEDINGS OF THE 20TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING (DISC
, 2006
"... We present a distributed algorithm that constructs an O(log n)approximate minimum spanning tree (MST) in any arbitrary network. This algorithm runs in time Õ(D(G) + L(G, w)) where L(G, w) is a parameter called the local shortest path diameter and D(G) is the (unweighted) diameter of the graph. Our ..."
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Cited by 35 (8 self)
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We present a distributed algorithm that constructs an O(log n)approximate minimum spanning tree (MST) in any arbitrary network. This algorithm runs in time Õ(D(G) + L(G, w)) where L(G, w) is a parameter called the local shortest path diameter and D(G) is the (unweighted) diameter of the graph. Our algorithm is existentially optimal (up to polylogarithmic factors), i.e., there exists graphs which need Ω(D(G) + L(G, w)) time to compute an Happroximation to the MST for any H ∈ [1, Θ(log n)]. Our result also shows that there can be a significant time gap between exact and approximate MST computation: there exists graphs in which the running time of our approximation algorithm is exponentially faster than the timeoptimal distributed algorithm that computes the MST. Finally, we show that our algorithm can be used to find an approximate MST in wireless networks and in random weighted networks in almost optimal Õ(D(G)) time.
Maximizing Capacity in MultiHop Cognitive Radio Networks Under the SINR Model
, 2010
"... Cognitive radio networks (CRNs) have the potential to utilize spectrum efficiently and are positioned to be the core technology for the nextgeneration multihop wireless networks. An important problem for such networks is its capacity. We study this problem for CRNs in the SINR (signaltointerfer ..."
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Cited by 17 (3 self)
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Cognitive radio networks (CRNs) have the potential to utilize spectrum efficiently and are positioned to be the core technology for the nextgeneration multihop wireless networks. An important problem for such networks is its capacity. We study this problem for CRNs in the SINR (signaltointerferenceandnoiseratio) model, which is considered to be a better characterization of interference (but also more difficult to analyze) than disk graph model. The main difficulties of this problem are twofold. First, SINR is a nonconvex function of transmission powers; an optimization problem in the SINR model is usually a nonconvex program and NPhard in general. Second, in the SINR model, scheduling feasibility and the maximum allowed flow rate on each link are determined by SINR at the physical layer. To maximize capacity, it is essential to follow a crosslayer approach; but joint optimization at physical (power control), link (scheduling), and network (flow routing) layers with the SINR function is inherently difficult. In this paper, we give a mathematical characterization of the joint relationship among these layers. We devise a solution procedure that provides a (1 − ε) optimal solution to this complex problem, where ε is the required accuracy. Our theoretical result offers a performance benchmark for any other algorithms developed for practical implementation. Using numerical results, we demonstrate the efficacy of the solution procedure and offer quantitative understanding on the interaction of power control, scheduling, and flow routing in a CRN.
Passive interference measurement in Wireless Sensor Networks,”
 in Proceedings of the 18th IEEE International Conference on Network Protocols (ICNP ’10),
, 2010
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SINR diagrams: Towards algorithmically usable SINR models of wireless networks
 In Proc. 28th Symp. on Principles of Distrib. Computing
, 2009
"... The rules governing the availability and quality of connections in a wireless network are described by physical models such as the signaltointerference & noise ratio (SINR) model. For a collection of simultaneously transmitting stations in the plane, it is possible to identify a reception zone ..."
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Cited by 15 (5 self)
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The rules governing the availability and quality of connections in a wireless network are described by physical models such as the signaltointerference & noise ratio (SINR) model. For a collection of simultaneously transmitting stations in the plane, it is possible to identify a reception zone for each station, consisting of the points where its transmission is received correctly. The resulting SINR diagram partitions the plane into a reception zone per station and the remaining plane where no station can be heard. SINR diagrams appear to be fundamental to understanding the behavior of wireless networks, and may play a key role in the development of suitable algorithms for such networks, analogous perhaps to the role played by Voronoi diagrams in the study of proximity queries and related issues in computational geometry. So far, however, the properties of SINR diagrams have not been studied systematically, and most algorithmic studies in wireless networking rely on simplified graphbased models such as the unit disk graph (UDG) model, which conveniently abstract away interferencerelated complications, and make it easier to handle algorithmic issues, but consequently fail to capture accurately some important aspects of wireless networks.
Sensor networks continue to puzzle: Selected open problems
 In Proc. 9th Internat. Conf. Distributed Computing and Networking (ICDCN
, 2008
"... Abstract. While several important problems in the field of sensor networks have already been tackled, there is still a wide range of challenging, open problems that merit further attention. We present five theoretical problems that we believe to be essential to understanding sensor networks. The goa ..."
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Cited by 14 (0 self)
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Abstract. While several important problems in the field of sensor networks have already been tackled, there is still a wide range of challenging, open problems that merit further attention. We present five theoretical problems that we believe to be essential to understanding sensor networks. The goal of this work is both to summarize the current state of research and, by calling attention to these fundamental problems, to spark interest in the networking community to attend to these and related problems in sensor networks.