Results 1  10
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38
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 142 (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.
A LogStar Distributed Maximal Independent Set Algorithm . . .
 PODC'08
, 2008
"... We present a novel distributed algorithm for the maximal independent set (MIS) problem. On growthbounded graphs (GBG) our deterministic algorithm finishes in O(log ∗ n) time, n being the number of nodes. In light of Linial’s Ω(log ∗ n) lower bound our algorithm is asymptotically optimal. Our algori ..."
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Cited by 76 (15 self)
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We present a novel distributed algorithm for the maximal independent set (MIS) problem. On growthbounded graphs (GBG) our deterministic algorithm finishes in O(log ∗ n) time, n being the number of nodes. In light of Linial’s Ω(log ∗ n) lower bound our algorithm is asymptotically optimal. Our algorithm answers prominent open problems in the ad hoc/sensor network domain. For instance, it solves the connected dominating set problem for unit disk graphs in O(log ∗ n) time, exponentially faster than the stateoftheart algorithm. With a new extension our algorithm also computes a δ + 1 coloring in O(log ∗ n) time, where δ is the maximum degree of the graph.
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 43 (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
A New Technique For Distributed Symmetry Breaking
 In Symp. on Principles of Distributed Computing
, 2010
"... We introduce MultiTrials, a new technique for symmetry breaking for distributed algorithms and apply it to various problems in general graphs. For instance, we present three randomized algorithms for distributed (vertex or edge) coloring improving on previous algorithms and showing a time/color tra ..."
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Cited by 34 (6 self)
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We introduce MultiTrials, a new technique for symmetry breaking for distributed algorithms and apply it to various problems in general graphs. For instance, we present three randomized algorithms for distributed (vertex or edge) coloring improving on previous algorithms and showing a time/color tradeoff. To get a ∆ + 1 coloring takes time O(log ∆ + √ log n). To obtain an O( ∆ + log 1+1 / log ∗ n n) coloring takes time O(log ∗ n). This is more than an exponential improvement in time for graphs of polylogarithmic degree. Our fastest algorithm works in constant time using O( ∆ log (c) n + log 1+1/c n) colors, where c denotes an arbitrary constant and log (c) n denotes the c times (recursively) applied logarithm to n. We also use the MultiTrials technique to compute network decompositions and to compute maximal independent set (MIS), obtaining new results for several graph classes.
Arbitrary Throughput Versus Complexity Tradeoffs in Wireless Networks using Graph Partitioning
, 2007
"... Several policies have recently been proposed for attaining the maximum throughput region, or a guaranteed fraction thereof, through dynamic link scheduling. Among these policies, the ones that attain the maximum throughput region require a computation time which is linear in the network size, and t ..."
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Cited by 32 (8 self)
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Several policies have recently been proposed for attaining the maximum throughput region, or a guaranteed fraction thereof, through dynamic link scheduling. Among these policies, the ones that attain the maximum throughput region require a computation time which is linear in the network size, and the ones that require constant or logarithmic computation time attain only certain fractions of the maximum throughput region. In contrast, in this paper we propose policies that can attain any desirable fraction of the maximum throughput region using a computation time that is largely independent of the network size. First, using a combination of graph partitioning techniques and lyapunov arguments, we propose a simple policy for tree topologies under the primary interference model that requires each link to exchange only 1 bit information with its adjacent links and approximates the maximum throughput region using a computation time that depends only on the maximum degree of nodes and the approximation factor. Then we develop a framework for attaining arbitrary close approximations for the maximum throughput region in arbitrary networks, and use this framework to obtain any desired tradeoff between throughput guarantees and computation times for a large class of networks and interference models. Specifically, given any ɛ> 0, the maximum throughput region can be approximated in these networks within a factor of 1 − ɛ using a computation time that depends only on the maximum node degree and ɛ.
Algorithmic Models of Interference in Wireless Ad Hoc and Sensor Networks
"... Abstract—Among the most critical issues of wireless ad hoc and sensor networks are energy consumption in general and interference in particular. The reduction of interference is consequently considered one of the foremost goals of topology control. Almost all of the related work however considers th ..."
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Cited by 14 (0 self)
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Abstract—Among the most critical issues of wireless ad hoc and sensor networks are energy consumption in general and interference in particular. The reduction of interference is consequently considered one of the foremost goals of topology control. Almost all of the related work however considers this issue implicitly: Low interference is often claimed to be a consequence of sparseness or low degree of the constructed topologies. This paper, in contrast, studies explicit definitions of interference. Various models of interference—both from a sendercentric and a receivercentric perspective—are proposed, compared, and analyzed with respect to their algorithmic properties and complexities. Index Terms—Algorithmic analysis, interference, modeling, network connectivity, network spanners, topology control.
Coloring Unstructured Wireless MultiHop Networks
 In PODC
, 2009
"... We present a randomized coloring algorithm for the unstructured radio network model, a model comprising autonomous nodes, asynchronous wakeup, no collision detection and an unknown but geometric network topology. The current stateoftheart coloring algorithm needs with high probability O(∆·log n) ..."
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Cited by 14 (4 self)
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We present a randomized coloring algorithm for the unstructured radio network model, a model comprising autonomous nodes, asynchronous wakeup, no collision detection and an unknown but geometric network topology. The current stateoftheart coloring algorithm needs with high probability O(∆·log n) time and uses O(∆) colors, where n and ∆ are the number of nodes in the network and the maximum degree, respectively; this algorithm requires knowledge of a linear bound on n and ∆. We improve this result in three ways: Firstly, we improve the time complexity, instead of the logarithmic factor we just need a polylogarithmic additive term; more specifically, our time complexity is O( ∆ + log ∆ · log n) given an estimate of n and ∆, and O( ∆ + log 2 n) without knowledge of ∆. Secondly, our vertex coloring algorithm needs ∆ + 1 colors only. Thirdly, our algorithm manages to do a distanced coloring with asymptotically optimal O(∆) colors for a constant d.
Sensor networks continue to puzzle: Selected open problems
 In Proc. 9th Internat. Conf. Distributed Computing and Networking (ICDCN
, 2008
"... Abstract. While several important problems in the field of sensor networks have already been tackled, there is still a wide range of challenging, open problems that merit further attention. We present five theoretical problems that we believe to be essential to understanding sensor networks. The goa ..."
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Cited by 14 (0 self)
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Abstract. While several important problems in the field of sensor networks have already been tackled, there is still a wide range of challenging, open problems that merit further attention. We present five theoretical problems that we believe to be essential to understanding sensor networks. The goal of this work is both to summarize the current state of research and, by calling attention to these fundamental problems, to spark interest in the networking community to attend to these and related problems in sensor networks.
Good quality virtual realization of unit ball graphs
 of Lecture Notes in Computer Science
, 2007
"... The quality of an embedding Φ: V ↦ → R 2 of a graph G = (V, E) into the Euclidean plane is the ratio of max{u,v}∈E Φ(u) − Φ(v)2 to min{u,v}�∈E Φ(u) − Φ(v)2. Given a graph G = (V, E), that is known to be a unit ball graph in fixed dimensional Euclidean space R d, we seek algorithms to compu ..."
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Cited by 12 (3 self)
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The quality of an embedding Φ: V ↦ → R 2 of a graph G = (V, E) into the Euclidean plane is the ratio of max{u,v}∈E Φ(u) − Φ(v)2 to min{u,v}�∈E Φ(u) − Φ(v)2. Given a graph G = (V, E), that is known to be a unit ball graph in fixed dimensional Euclidean space R d, we seek algorithms to compute an embedding Φ: V ↦ → R 2 of best (smallest) quality. Note that G comes with no associated geometric information and in this setting, related problems such as recognizing if G is a unit disk graph (UDG), are NPhard. While any connected unit disk graph (UDG) has a 2dimensional embedding with quality between 1/2 and 1, as far as we know, Vempala’s random projection approach (FOCS 1998) provides the best quality bound of O(log 3 n · √ log log n) for this problem. This paper presents a simple, combinatorial algorithm for computing a O(log 2.5 n)quality 2dimensional embedding of a given graph, that is known to be a UBG in fixed dimensional Euclidean space R d. If the embedding is allowed to reside in higher dimensional space, we obtain improved results: a quality2 embedding in R O(d log d). The first step of our algorithm constructs a “growthrestricted approximation ” of the given UBG. While such a construction is trivial if the UBG comes with a geometric representation, we are not aware of any other algorithm that can perform this step without geometric information. Construction of a growthrestricted approximation permits us to bypass the standard and costly technique of solving a linear program with exponentially many “spreading constraints. ” As a side effect of our construction, we get a constantfactor approximation to the minimum clique cover problem for UBGs, described without geometry. The second step of our algorithm combines the probabilistic decomposition of growthrestricted graphs due to Lee and Krauthgamer (STOC 2003) with Rao’s embedding algorithm for planar graphs (SoCG 1999) to obtain a (k, O ( √ log n))volume respecting embedding of growthrestricted graphs. Our problem is a version of the well known localization problem in wireless sensor networks, in which network nodes are required to compute virtual 2dimensional Euclidean coordinates given little or (as in our case) no geometric information.
Local PTAS for Independent Set and Vertex Cover in Location Aware Unit Disk Graphs
 In Proceedings of the 4th IEEE/ACM International Conference on Distributed Computing in Sensor Systems (DCOSS
, 2008
"... Abstract. We present the first local approximation schemes for maximum independent set and minimum vertex cover in unit disk graphs. In the graph model we assume that each node knows its geographic coordinates in the plane (location aware nodes). Our algorithms are local in the sense that the status ..."
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Cited by 8 (1 self)
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Abstract. We present the first local approximation schemes for maximum independent set and minimum vertex cover in unit disk graphs. In the graph model we assume that each node knows its geographic coordinates in the plane (location aware nodes). Our algorithms are local in the sense that the status of each node v (whether or not v is in the computed set) depends only on the vertices which are a constant number of hops away from v. This constant is independent of the size of the network. We give upper bounds for the constant depending on the desired approximation ratio. We show that the processing time which is necessary in order to compute the status of a single vertex is bounded by a polynomial in the number of vertices which are at most a constant number of vertices away from it. Our algorithms give the best possible approximation ratios for this setting. The technique which we use to obtain the algorithm for vertex cover can also be employed for constructing the first global PTAS for this problem in unit disk graph which does not need the embedding of the graph as part of the input. 1.