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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
Oblivious interference scheduling
 IN PROCEEDINGS OF THE 28THANNUAL ACM SYMPOSIUM ON PRINCIPLES OF DISTRIBUTED COMPUTING (PODC
, 2009
"... In the interference scheduling problem, one is given a set of n communication requests described by pairs of points from a metric space. The points correspond to devices in a wireless network. In the directed version of the problem, each pair of points consists of a dedicated sending and a dedicated ..."
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Cited by 45 (12 self)
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In the interference scheduling problem, one is given a set of n communication requests described by pairs of points from a metric space. The points correspond to devices in a wireless network. In the directed version of the problem, each pair of points consists of a dedicated sending and a dedicated receiving device. In the bidirectional version the devices within a pair shall be able to exchange signals in both directions. In both versions, each pair must be assigned a power level and a color such that the pairs in each color class can communicate simultaneously at the specified power levels. The feasibility of simultaneous communication within a color class is defined in terms of the Signal to Interference Plus Noise Ratio (SINR) that compares the strength of a signal at a receiver to the sum of the strengths of other signals. This is commonly referred to as the “physical model ” and is the established way of modelling interference in the engineering community. The objective is to minimize the number of colors as this corresponds to the time needed to schedule all requests. We study oblivious power assignments in which the power value of a pair only depends on the distance between the points of this pair. We prove that oblivious power assignments cannot yield approximation ratios better than Ω(n) for the directed version of the problem, which is the worst possible performance guarantee
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 44 (3 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
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 36 (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.
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