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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 49 (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
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 35 (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.
Wireless Capacity with Oblivious Power in General Metrics
"... The capacity of a wireless network is the maximum possible amount of simultaneous communication, taking interference into account. Formally, we treat the following problem. Given is a set of links, each a senderreceiver pair located in a metric space, and an assignment of power to the senders. We s ..."
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Cited by 27 (7 self)
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The capacity of a wireless network is the maximum possible amount of simultaneous communication, taking interference into account. Formally, we treat the following problem. Given is a set of links, each a senderreceiver pair located in a metric space, and an assignment of power to the senders. We seek a maximum subset of links that are feasible in the SINR model: namely, the signal received on each link should be larger than the sum of the interferences from the other links. We give a constantfactor approximation that holds for any lengthmonotone, sublinear power assignment and any distance metric. We use this to give essentially tight characterizations of capacity maximization under power control using oblivious power assignments. Specifically, we show that the mean
Approximation algorithms for secondary spectrum auctions
 In Proc. 23rd Symp. Parallelism in Algorithms and Architectures (SPAA
, 2011
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Nearly optimal bounds for distributed wireless scheduling in the sinr model. Arxiv preprint arXiv:1104.5200
, 2011
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Online Capacity Maximization in Wireless Networks ∗
"... In this paper we study a dynamic version of capacity maximization in the physical model of wireless communication. In our model, requests for connections between pairs of points in Euclidean space of constant dimension d arrive iteratively over time. When a new request arrives, an online algorithm n ..."
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Cited by 13 (4 self)
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In this paper we study a dynamic version of capacity maximization in the physical model of wireless communication. In our model, requests for connections between pairs of points in Euclidean space of constant dimension d arrive iteratively over time. When a new request arrives, an online algorithm needs to decide whether or not to accept the request and to assign one out of k channels and a transmission power to the channel. Accepted requests must satisfy constraints on the signaltointerferenceplusnoise (SINR) ratio. The objective is to maximize the number of accepted requests. Using competitive analysis we study algorithms using distancebased power assignments, for which the power of a request relies only on the distance between the points. Such assignments are inherently local and particularly useful in distributed settings. We first focus on the case of a single channel. For request sets with spatial lengths in [1, ∆] and duration in [1, Γ] we derive a lower bound of Ω(Γ · ∆ d/2) on the competitive ratio of any deterministic online algorithm using a distancebased power assignment. Our main“ result is a nearoptimal deterministic algorithm that is O Γ · ∆ (d/2)+εcompetitive, for any constant ε> 0. Our algorithm for a single channel can be generalized to k channels. “ It can be adjusted to yield a competitive ratio of O k · Γ 1/k′ · ∆ (d/2k′ ′ ”
On the Power of Uniform Power: Capacity of Wireless Networks with Bounded Resources
"... Abstract. The throughput capacity of arbitrary wireless networks under the physical Signal to Interference Plus Noise Ratio (SINR) model has received much attention in recent years. In this paper, we investigate the question of how much the worstcase performance of uniform and nonuniform power ass ..."
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Cited by 12 (3 self)
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Abstract. The throughput capacity of arbitrary wireless networks under the physical Signal to Interference Plus Noise Ratio (SINR) model has received much attention in recent years. In this paper, we investigate the question of how much the worstcase performance of uniform and nonuniform power assignments differ under constraints such as a bound on the area where nodes are distributed or restrictions on the maximum power available. We determine the maximum factor by which a nonuniform power assignment can outperform the uniform case in the SINR model. More precisely, we prove that in onedimensional settings the capacity of a nonuniform assignment exceeds a uniform assignment by at most a factor of O(log Lmax) when the length of the network is Lmax. In twodimensional settings, the uniform assignment is at most a factor of O(log Pmax) worse than the nonuniform assignment if the maximum power is Pmax. We provide algorithms that reach this capacity in both cases. Due to lower bound examples in previous work, these results are tight in the sense that there are networks where the lack of power control causes a performance loss in the order of these factors. As a consequence, engineers and researchers may prefer the uniform model due to its simplicity if this degree of performance deterioration is acceptable. 1
Wireless Connectivity and Capacity
"... Given n wireless transceivers located in a plane, a fundamental problem in wireless communications is to construct a strongly connected digraph on them such that the constituent links can be scheduled in fewest possible time slots, assuming the SINR model of interference. In this paper, we provide a ..."
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Cited by 11 (4 self)
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Given n wireless transceivers located in a plane, a fundamental problem in wireless communications is to construct a strongly connected digraph on them such that the constituent links can be scheduled in fewest possible time slots, assuming the SINR model of interference. In this paper, we provide an algorithm that connects an arbitrary point set in O(log n) slots, improving on the previous best bound of O(log 2 n) due to Moscibroda. This is complemented with a superconstant lower bound on our approach to connectivity. An important feature is that the algorithms allow for bidirectional (halfduplex) communication. One implication of this result is an improved bound of Ω(1 / log n) on the worstcase capacity of wireless networks, matching the best bound known for the extensively studied averagecase. We explore the utility of oblivious power assignments, and show that essentially all such assignments result in a worst case bound of Ω(n) slots for connectivity. This rules out a recent claim of a O(log n) bound using oblivious power. On the other hand, using our result we show that O(min(log ∆, log n · (log n + log log ∆))) slots suffice, where ∆ is the ratio between the largest and the smallest links in a minimum spanning tree of the points. Our results extend to the related problem of minimum latency aggregation scheduling, where we show that aggregation scheduling with O(log n) latency is possible, improving upon the previous best known latency of O(log 3 n). We also initiate the study of network design problems in the SINR model beyond strong connectivity, obtaining similar bounds for biconnected and kedge connected structures. 1
Scheduling in Wireless Networks with RayleighFading Interference
"... We study algorithms for wireless spectrum access of n communication requests when interference conditions are given by the Rayleighfading model. This model extends the recently popular deterministic interference model based on the signaltointerferenceplusnoise ratio (SINR) using stochastic prop ..."
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Cited by 9 (3 self)
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We study algorithms for wireless spectrum access of n communication requests when interference conditions are given by the Rayleighfading model. This model extends the recently popular deterministic interference model based on the signaltointerferenceplusnoise ratio (SINR) using stochastic propagation to address fading effects observed in reality. We consider worstcase approximation guarantees for the two standard problems of capacity maximization (maximize the expected number of successful transmissions in a single slot) and latency minimization (minimize the expected number of slots until all transmissions were successful). Our main result is a generic reduction of Rayleigh fading to the deterministic SINR model. It allows to apply existing algorithms for the nonfading model in the Rayleighfading scenario while losing only a factor of O(log ∗ n) in the approximation guarantee. This way, we obtain the first approximation guarantees for Rayleigh fading and, more fundamentally, show that nontrivial stochastic fading effects can be successfully handled using existing and future techniques for the nonfading model. Using a more detailed argument, a similar result applies even for distributed and gametheoretic capacity maximization approaches. For example, it allows to show that regret learning yields an O(log ∗ n)approximation with uniform power assignments. Our analytical treatment is supported by simulations illustrating the performance of regret learning and, more generally, the relationship between both models.