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14
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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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
Link scheduling in local interference models
 In AlgoSensors
, 2008
"... Abstract. Choosing an appropriate interference model is crucial for link scheduling problems in sensor networks. While graphbased interference models allow for distributed and purely local coloring approaches which lead to many interesting results, a more realistic and widely agreed on model such a ..."
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Cited by 6 (0 self)
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Abstract. Choosing an appropriate interference model is crucial for link scheduling problems in sensor networks. While graphbased interference models allow for distributed and purely local coloring approaches which lead to many interesting results, a more realistic and widely agreed on model such as the signaltonoiseplusinterference ratio (SINR) inherently makes scheduling radio transmission a nonlocal task, and thus impractical for the development of distributed and scalable scheduling protocols in sensor networks. In this work, we focus on interference models that are local in the sense that admissibility of transmissions only depends on local concurrent transmissions, and correct with respect to the geometric SINR model. In our analysis, we show lower bounds on the limitations that these restrictions impose an any such model as well as approximation results for greedy scheduling algorithms in a class of these models. 1
On the Transmission Scheduling of Wireless Networks under SINR Constraints
, 2010
"... In this paper we study a joint transmission scheduling and power control problem that arises in wireless networks. The goal is to assign time slots (or channels) and transmitting powers to communication links such that all communication requests are processed correctly, specified QualityofService ..."
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In this paper we study a joint transmission scheduling and power control problem that arises in wireless networks. The goal is to assign time slots (or channels) and transmitting powers to communication links such that all communication requests are processed correctly, specified QualityofService (QoS) requirements are met, and the number of required time slots is minimized. The first main result proves that the problem, also known as the wireless scheduling problem, is NPhard. We then solve a mixedinteger linear programming (MILP) formulation of the problem with Branch & Bound (B&B) and Cutting Plane (CP) approaches. We enhance the computational performance of these schemes with heuristic procedures that provide tighter upper and lower bounds. We close with an extensive computational study, which shows that despite the complexity of the problem, the proposed methodology scales to problems of nontrivial size. Our algorithms can therefore serve as a benchmark for the performance evaluation of heuristic or distributed algorithms that aim to find nearoptimal solutions without information about the whole network.
Joint Link Scheduling and Topology Control for Wireless Sensor Networks with SINR Constraints
"... This chapter studies the joint link scheduling and topology control problems in wireless sensor networks. Given arbitrarily located sensor nodes on a plane, the task is to schedule all the wireless links (each representing a wireless transmission) between adjacent sensors using a minimum number of t ..."
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Cited by 3 (2 self)
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This chapter studies the joint link scheduling and topology control problems in wireless sensor networks. Given arbitrarily located sensor nodes on a plane, the task is to schedule all the wireless links (each representing a wireless transmission) between adjacent sensors using a minimum number of timeslots. There are two requirements for these problems: first, all the links must satisfy a certain property, such as that the wireless links form a data gathering tree towards the sink node; second, all the links simultaneously scheduled in the same timeslot must satisfy the SINR constraints. This chapter focuses on various scheduling algorithms for both arbitrarily constructed link topologies and the data gathering tree topology. We also discuss possible research directions.
Bounding Interference in Wireless Ad Hoc Networks with Nodes in Random Position
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 2015
"... Given a set of positions for wireless nodes, the interference minimization problem is to assign a transmission radius (i.e., a power level) to each node such that the resulting communication graph is connected, while minimizing the maximum (respectively, average) interference. We consider the model ..."
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Cited by 2 (0 self)
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Given a set of positions for wireless nodes, the interference minimization problem is to assign a transmission radius (i.e., a power level) to each node such that the resulting communication graph is connected, while minimizing the maximum (respectively, average) interference. We consider the model introduced by von Rickenbach et al. (2005), in which each wireless node is represented by a point in Euclidean space on which is centred a transmission range represented by a ball, and edges in the corresponding graph are symmetric. The problem is NPcomplete in two or more dimensions (Buchin 2008) and no polynomialtime approximation algorithm is known. We show how to solve the problem efficiently in settings typical for wireless ad hoc networks. If nodes are represented by a set P of n points selected uniformly and independently at random over a ddimensional rectangular region, then the topology given by the closure of the Euclidean minimum spanning tree of P has O(logn) maximum interference with high probability and O(1) expected interference. We extend the first bound to a general class of communication graphs over a broad set of probability distributions. We present a local algorithm that constructs a graph from this class; this is the first local algorithm to provide an upper bound on expected maximum interference. Finally, we disprove a conjecture of Devroye and Morin (2012) relating the maximum interference of the Euclidean minimum spanning tree to the optimal maximum interference attainable.
On the complexity of scheduling with power control in geometric SINR
, 2009
"... Although being a very fundamental problem in the field of wireless networks, the complexity of transmission scheduling with power control in the Geometric SINR model is still unknown. In this article, we show that the joint problem of finding transmission powers and scheduling the transmissions is N ..."
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Although being a very fundamental problem in the field of wireless networks, the complexity of transmission scheduling with power control in the Geometric SINR model is still unknown. In this article, we show that the joint problem of finding transmission powers and scheduling the transmissions is NPhard if the available powers are bounded, independent of the actual bounds. This also implies that scheduling with a finite number of power levels is NPhard. 1
A TIGHT BOUND ON THE MAXIMUM INTERFERENCE OF RANDOM SENSORS IN THE HIGHWAY MODEL
, 2010
"... Abstract. Consider n sensors whose positions are represented by n uniform, independent and identically distributed random variables assuming values in the open unit interval (0, 1). A natural way to guarantee connectivity in the resulting sensor network is to assign to each sensor as its range, the ..."
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Abstract. Consider n sensors whose positions are represented by n uniform, independent and identically distributed random variables assuming values in the open unit interval (0, 1). A natural way to guarantee connectivity in the resulting sensor network is to assign to each sensor as its range, the maximum of the two possible distances to its two neighbors. The interference at a given sensor is defined as the number of sensors that have this sensor within their range. In this paper we prove that the expected maximum interference of the sensors is Θ ( √ ln n). 1
On the Complexity of the Minimum Latency Scheduling Problem on the Euclidean Plane ∗
, 2012
"... We show NPhardness of the minimum latency scheduling (MLS) problem under the physical model of wireless networking. In this model a transmission is received successfully if the Signal to InterferenceplusNoise Ratio (SINR), is above a given threshold. In the minimum latency scheduling problem, the ..."
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We show NPhardness of the minimum latency scheduling (MLS) problem under the physical model of wireless networking. In this model a transmission is received successfully if the Signal to InterferenceplusNoise Ratio (SINR), is above a given threshold. In the minimum latency scheduling problem, the goal is to assign a time slot and power level to each transmission, so that all the messages are received successfully, and the number of distinct times slots is minimized. Despite its seeming simplicity and several previous hardness results for various settings of the minimum latency scheduling problem, it has remained an open question whether or not the minimum latency scheduling problem is NPhard, when the nodes are placed in the Euclidean plane and arbitrary power levels can be chosen for the transmissions. We resolve this open question for all path loss exponent values α ≥ 3. 1
RELIABILITY and STATISTICS in TRANSPORTATION and COMMUNICATION 2012
"... One of the major challenges in creating intelligent transportation systems has been and remains the task of object localization (locating) in motion. To some extent, it can be solved by equipping all such objects with global position system (GPS). Unfortunately, in densely builtup urban areas, loc ..."
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One of the major challenges in creating intelligent transportation systems has been and remains the task of object localization (locating) in motion. To some extent, it can be solved by equipping all such objects with global position system (GPS). Unfortunately, in densely builtup urban areas, localization based on GPS only produces a large error, or simply becomes impossible. New opportunities arise for the localization due to the rapidly emerging in the last decade concept of a wireless adhoc network (VANET). Nodes of such network are able to localize themselves being equipped with shortwave communication devices. In addition, they can use some reference points on the ground. Besides mutual exchange of information between the moving objects, such network, allows to estimate potential distance between these objects measuring received signal level. It makes possible to construct a graph of distances in which nodes are the localization objects, and edges estimates of the distances between pairs of nodes. Due to the known coordinates of individual nodes (anchors), it is possible to determine the location of all (or part) of the remaining nodes of the graph. However, despite abundance of wellknown algorithms for solving the problem of localization and significant research efforts, there are still many issues that currently are addressed only partially. Unfortunately, known solutions cannot simultaneously take into account many factors affecting localization quality. For example, environment affecting radio signal, no line of sight between objects, a small number of anchors, high mobility objects, etc In this paper, we propose localization approach based on the graph mapped distances on the road map, constructed on the GIS data basis. In fact, problem is reduced to distance graph embedding into the graph representing GIS data of the area. In this case, it is possible to localize objects, even if only one reference point is available.