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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.
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).
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
Wireless Communication is in APX
 In Proc. 36th International Colloquium on Automata, Languages and Programming (ICALP
, 2009
"... Abstract. In this paper we address a common question in wireless communication: How long does it take to satisfy an arbitrary set of wireless communication requests? This problem is known as the wireless scheduling problem. Our main result proves that wireless scheduling is in APX. In addition we pr ..."
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Cited by 31 (5 self)
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Abstract. In this paper we address a common question in wireless communication: How long does it take to satisfy an arbitrary set of wireless communication requests? This problem is known as the wireless scheduling problem. Our main result proves that wireless scheduling is in APX. In addition we present a robustness result, showing that constant parameter and model changes will modify the result only by a constant. 1
A constant approximation algorithm for link scheduling in arbitrary networks under physical interference model
 Proc. ACM FOWANC
, 2009
"... Link scheduling is crucial in improving the throughput in wireless networks and it has been widely studied under various interference models. In this paper, we study the link scheduling problem under physical interference model where all senders of the links transmit at a given power P and a link ca ..."
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Cited by 13 (4 self)
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Link scheduling is crucial in improving the throughput in wireless networks and it has been widely studied under various interference models. In this paper, we study the link scheduling problem under physical interference model where all senders of the links transmit at a given power P and a link can transmit successfully if and only if the SignaltoInterferenceplusNoiseRatio (SINR) at the corresponding receiver is at least a certain threshold. The link scheduling problem is to find a maximum “independent set ” (MIS) of links, i.e., the maximum number of links that can transmit successfully in one timeslot, given a set of input links. This problem has been shown to be NPhard [10]. Here we propose the first link scheduling algorithm with a constant approximation ratio for arbitrary background noise N ≥ 0. When each link l has a weight w(l)> 0, we propose a method for weighted MIS with approximation ratio O(min(log maxl∈L w(l) minl∈L w(l) , log maxl∈L ‖l‖)), where‖l‖ minl∈L ‖l‖ is the Euclidean length of a link l.
Adaptive Instantiation of the Protocol Interference Model in Wireless Networked Sensing and Control
"... Interference model is the basis of MAC protocol design in wireless networked sensing and control, and it directly affects the efficiency and predictability of wireless messaging. To exploit the strengths of both the physical and the protocol interference models, we analyze how network traffic, link ..."
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Cited by 12 (8 self)
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Interference model is the basis of MAC protocol design in wireless networked sensing and control, and it directly affects the efficiency and predictability of wireless messaging. To exploit the strengths of both the physical and the protocol interference models, we analyze how network traffic, link length, and wireless signal attenuation affect the optimal instantiation of the protocol model. We also identify the inherent tradeoff between reliability and throughput in the model instantiation. Our analysis sheds light on the open problem of efficiently optimizing the protocol model instantiation. Based on the analytical results, we propose the physicalratioK (PRK) interference model as a reliabilityoriented instantiation of the protocol model. Via analysis, simulation, and testbedbased measurement, we show that PRKbased scheduling achieves a network throughput very close to (e.g., 95%) what is enabled by physicalmodelbased scheduling while ensuring the required packet delivery reliability. The PRK model inherits both the high fidelity of the physical model and the locality of the protocol model, thus it is expected to be suitable for distributed protocol design. These findings shed new light on wireless interference models; they also suggest new approaches to MAC protocol design in the presence of uncertainties in traffic patterns and application QoS requirements.
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 11 (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′ ′ ”
MinimumLatency Aggregation Scheduling in Wireless Sensor Networks under Physical Interference Model
"... is a problem of fundamental importance in wireless sensor networks. There however has been very little effort spent on designing algorithms to achieve sufficiently fast data aggregation under the physical interference model which is a more realistic model than traditional protocol interference model ..."
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Cited by 11 (4 self)
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is a problem of fundamental importance in wireless sensor networks. There however has been very little effort spent on designing algorithms to achieve sufficiently fast data aggregation under the physical interference model which is a more realistic model than traditional protocol interference model. In particular, a distributed solution to the problem under the physical interference model is challenging because of the need for globalscale information to compute the cumulative interference at any individual node. In this paper, we propose a distributed algorithm that solves the MLAS problem under the physical interference model in networks of arbitrary topology in O(K) time slots, where K is the logarithm of the ratio between the lengths of the longest and shortest links in the network. We also give a centralized algorithm to serve as a benchmark for comparison purposes, which aggregates data from all sources in O(log 3 (n)) time slots (where n is the total number of nodes). This is the current best algorithm for the problem in the literature. The distributed algorithm partitions the network into cells according to the value K, thus obviating the need for global information. The centralized algorithm strategically combines our aggregation tree construction algorithm with the nonlinear power assignment strategy in [13]. We prove the correctness and efficiency of our algorithms, and conduct empirical studies under realistic settings to validate our analytical results. I.
Approximation Algorithms for Wireless Link Scheduling with SINRbased Interference
"... In this paper, we consider the classical problem of link scheduling in wireless networks under an accurate interference model, in which correct packet reception at a receiver node depends on the signal to interference plus noise ratio (SINR). While most previous work on wireless networks has addres ..."
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Cited by 10 (1 self)
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In this paper, we consider the classical problem of link scheduling in wireless networks under an accurate interference model, in which correct packet reception at a receiver node depends on the signal to interference plus noise ratio (SINR). While most previous work on wireless networks has addressed the scheduling problem using simplistic graphbased or distancebased interference models, a few recent papers have investigated scheduling with SINRbased interference models. However, these papers have either used approximations to the SINR model or have ignored important aspects of the problem. We study the problem of wireless link scheduling under the exact SINR model, and present the first known true approximation algorithms for transmission scheduling under the exact model. We also introduce an algorithm with a proven approximation bound with respect to the length of the optimal schedule under primary interference. As an aside, our study identifies a class of “difficult to schedule” links, which hinder the derivation of tighter approximation bounds. Furthermore, we characterize conditions under which scheduling under SINRbased interference is within a constant factor from optimal under primary interference, which implies that secondary interference only degrades performance by a constant factor in these situations.
Exact and approximate link scheduling algorithms under the physical interference model
 In Proc. 5th SIGACTSIGOPS International Workshop on Foundation of Mobile computing (DIALMPOMC
, 2008
"... Given n arbitrarily distributed singlehop wireless links, using the physical interference model, the objective is to minimize the scheduling length. This is an open problem (Problem 1) proposed by Locher et al. [21]. In this paper, we solve this open problem at the cost of moderately exponential ti ..."
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Cited by 9 (3 self)
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Given n arbitrarily distributed singlehop wireless links, using the physical interference model, the objective is to minimize the scheduling length. This is an open problem (Problem 1) proposed by Locher et al. [21]. In this paper, we solve this open problem at the cost of moderately exponential time. Specifically, this paper gives two classes of exact and approximate link scheduling algorithms, one based on the somewhat straightforward link independent set covering, and the other on counting the number of set covers. Let pn ( ) denote the time of checking whether the spectral radius of an irreducible nonnegative matrix is smaller than 1 or not, then the time complexity for the set covering based exact algorithm n ( n /2) is O(2) , whereas the proposed counting based exact scheduling algorithm called ESA_MLSAT needs only time n 2 O(3 ⋅n⋅log n⋅ p ( n)) with polynomial space. If exponential space is allowed, the time complexity can be further reduced n 2 to O(2 ⋅n⋅log n⋅ p ( n)). The time complexity for the set covering n based approximate algorithm is O( ( n /2) ⋅log n ⋅ p ( n)) with approximation ratio O(log n). The time complexity of the first 2 counting based approximation algorithm is O ( n poly log ( n)) with approximation ratio On ( log n), the time complexity of the second counting based approximation algorithm is k−1 1+ log3⋅log