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115
AdHoc Networks Beyond Unit Disk Graphs
, 2003
"... In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer ..."
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Cited by 140 (11 self)
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In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1. We show that  in comparison to the cost known on Unit Disk Graphs  the complexity results in this model contain the additional factor 1/d&sup2;. We prove that in Quasi Unit Disk Graphs flooding is an asymptotically messageoptimal routing technique, provide a geometric routing algorithm being more efficient above all in dense networks, and show that classic geometric routing is possible with the same performance guarantees as for Unit Disk Graphs if d 1/ # 2.
Topology control meets sinr: the scheduling complexity of arbitrary topologies
 in Proceedings of ACM MobiHoc
, 2006
"... To date, topology control in wireless ad hoc and sensor networks—the study of how to compute from the given communication network a subgraph with certain beneficial properties—has been considered as a static problem only; the time required to actually schedule the links of a computed topology with ..."
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Cited by 103 (9 self)
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To date, topology control in wireless ad hoc and sensor networks—the study of how to compute from the given communication network a subgraph with certain beneficial properties—has been considered as a static problem only; the time required to actually schedule the links of a computed topology without message collision was generally ignored. In this paper we analyze topology control in the context of the physical SignaltoInterferenceplusNoiseRatio (SINR) model, focusing on the question of how and how fast the links of a resulting topology can actually be realized over time. For this purpose, we define and study a generalized version of the SINR model and obtain theoretical upper bounds on the scheduling complexity of arbitrary topologies in wireless networks. Specifically, we prove that even in worstcase networks, if the signals are transmitted with correctly assigned transmission power levels, the number of time slots required to successfully schedule all links of an arbitrary topology is proportional to the squared logarithm of the number of network nodes times a previously defined static interference measure. Interestingly, although originally considered without explicit accounting for signal collision in the SINR model, this static interference measure plays an important role in the analysis of link scheduling with physical link interference. Our result thus bridges the gap between static graphbased interference models and the physical SINR model. Based on these results, we also show that when it comes to scheduling, requiring the communication links to be symmetric may imply significantly higher costs as opposed to topologies allowing unidirectional links.
Allocating Dynamic TimeSpectrum Blocks In Cognitive Radio Networks
, 2007
"... A number of studies have shown the abundance of unused spectrum in the TV bands. This is in stark contrast to the overcrowding of wireless devices in the ISM bands. A recent trend to alleviate this disparity is the design of Cognitive Radios, which constantly sense the spectrum and opportunistically ..."
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Cited by 95 (2 self)
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A number of studies have shown the abundance of unused spectrum in the TV bands. This is in stark contrast to the overcrowding of wireless devices in the ISM bands. A recent trend to alleviate this disparity is the design of Cognitive Radios, which constantly sense the spectrum and opportunistically utilize unused frequencies in the TV bands. In this paper, we introduce the concept of a timespectrum block to model spectrum reservation, and use it to present a theoretical formalization of the spectrum allocation problem in cognitive radio networks. We present a centralized and a distributed protocol for spectrum allocation and show that these protocols are close to optimal in most scenarios. We have implemented the distributed protocol in QualNet and show that our analysis closely matches the simulation results.
Complexity in geometric sinr
 In MobiHoc
, 2007
"... In this paper we study the problem of scheduling wireless links in the geometric SINR model, which explicitly uses the fact that nodes are distributed in the Euclidean plane. We present the first NPcompleteness proofs in such a model. In particular, we prove two problems to be NPcomplete: Scheduli ..."
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Cited by 77 (2 self)
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In this paper we study the problem of scheduling wireless links in the geometric SINR model, which explicitly uses the fact that nodes are distributed in the Euclidean plane. We present the first NPcompleteness proofs in such a model. In particular, we prove two problems to be NPcomplete: Scheduling and OneShot Scheduling. The first problem consists in finding a minimumlength schedule for a given set of links. The second problem receives a weighted set of links as input and consists in finding a maximumweight subset of links to be scheduled simultaneously in one shot. In addition to the complexity proofs, we devise an approximation algorithm for each problem.
Capacity of Arbitrary Wireless Networks
, 2009
"... In this work we study the problem of determining the throughput capacity of a wireless network. We propose a scheduling algorithm to achieve this capacity within an approximation factor. Our analysis is performed in the physical interference model, where nodes are arbitrarily distributed in Euclide ..."
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Cited by 73 (7 self)
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In this work we study the problem of determining the throughput capacity of a wireless network. We propose a scheduling algorithm to achieve this capacity within an approximation factor. Our analysis is performed in the physical interference model, where nodes are arbitrarily distributed in Euclidean space. We consider the problem separately from the routing problem and the power control problem, i.e., all requests are singlehop, and all nodes transmit at a fixed power level. The existing solutions to this problem have either concentrated on specialcase topologies, or presented optimality guarantees which become arbitrarily bad (linear in the number of nodes) depending on the network’s topology. We propose the first scheduling algorithm with approximation guarantee independent of the topology of the network. The algorithm has a constant approximation guarantee for the problem of maximizing the number of links scheduled in one timeslot. Furthermore, we obtain a O(log n) approximation for the problem of minimizing the number of time slots needed to schedule a given set of requests. Simulation results indicate that our algorithm does not only have an exponentially better approximation ratio in theory, but also achieves superior performance in various practical network scenarios. Furthermore, we prove that the analysis of the algorithm is extendable to higherdimensional Euclidean spaces, and to more realistic boundeddistortion spaces, induced by nonisotropic signal distortions. Finally, we show that it is NPhard to approximate the scheduling problem to within n 1−ε factor, for any constant ε> 0, in the nongeometric SINR model, in which pathloss is independent of the Euclidean coordinates of the nodes.
A Measurement Study of Interference Modeling and Scheduling in LowPower Wireless Networks
"... Accurate interference models are important for use in transmission scheduling algorithms in wireless networks. In this work, we perform extensive modeling and experimentation on two 20node TelosB motes testbeds – one indoor and the other outdoor – to compare a suite of interference models for their ..."
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Cited by 71 (1 self)
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Accurate interference models are important for use in transmission scheduling algorithms in wireless networks. In this work, we perform extensive modeling and experimentation on two 20node TelosB motes testbeds – one indoor and the other outdoor – to compare a suite of interference models for their modeling accuracies. We first empirically build and validate the physical interference model via a packet reception rate vs. SINR relationship using a measurement driven method. We then similarly instantiate other simpler models, such as hopbased, rangebased, protocol model, etc. The modeling accuracies are then evaluated on the two testbeds using transmission scheduling experiments. We observe that while the physical interference model is the most accurate, it is still far from perfect, providing a 90percentile error about 2025 % (and 80 percentile error 712%), depending on the scenario. The accuracy of the other models is worse and scenariospecific. The second best model trails the physical model by roughly 1218 percentile points for similar accuracy targets. Somewhat similar throughput performance differential between models is also observed when used with greedy scheduling algorithms. Carrying on further, we look closely into the the two incarnations of the physical model – ‘thresholded ’ (conservative, but typically considered in literature) and ‘graded ’ (more realistic). We show via solving the one shot scheduling problem, that the graded version can improve ‘expected throughput ’ over the thresholded version by scheduling imperfect links. Categories and Subject Descriptors C.2.1 [Network architecture and design]: Wireless communication;
Protocol design beyond graphbased models
 In Proc. of HotNets
, 2006
"... In this paper we shed new light on the fundamental gap between graphbased models used by protocol designers and fading channel models used by communication theorists in wireless networks. We experimentally demonstrate that graphbased models capture realworld phenomena inadequately. Consequentiall ..."
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Cited by 56 (5 self)
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In this paper we shed new light on the fundamental gap between graphbased models used by protocol designers and fading channel models used by communication theorists in wireless networks. We experimentally demonstrate that graphbased models capture realworld phenomena inadequately. Consequentially, we advocate studying models beyond graphs even for protocoldesign. In the main part of the paper we present an archetypal multihop situation. We show that the theoretical limits of any protocol which obeys the laws of graphbased models can be broken by a protocol explicitly defined for the physical model. Finally, we discuss possible applications, from data gathering to media access control. 1
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
Modeling sensor networks
, 2008
"... In order to develop algorithms for sensor networks and in order to give mathematical correctness and performance proofs, models for various aspects of sensor networks are needed. This chapter presents and discusses currently used models for sensor networks. Generally, finding good models is a challe ..."
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Cited by 44 (5 self)
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In order to develop algorithms for sensor networks and in order to give mathematical correctness and performance proofs, models for various aspects of sensor networks are needed. This chapter presents and discusses currently used models for sensor networks. Generally, finding good models is a challenging task. On the one hand, a
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 43 (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