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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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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.
Aligned virtual coordinates for greedy routing in WSNs
 Proc. IEEE Int. Conf. on Mobile Adhoc and Sensor Systems
, 2006
"... Abstract — Geographic routing provides relatively good performance at a much lower overhead than conventional routing protocols such as AODV. However, the performance of these protocols is impacted by physical voids, and localization errors. Accordingly, virtual coordinate systems (VCS) were propose ..."
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Abstract — Geographic routing provides relatively good performance at a much lower overhead than conventional routing protocols such as AODV. However, the performance of these protocols is impacted by physical voids, and localization errors. Accordingly, virtual coordinate systems (VCS) were proposed as an alternative approach that is resilient to localization errors and that naturally routes around physical voids. However, we show that VCS is vulnerable to different forms of the void problem and the performance of greedy routing on VCS is worse than that of geographic forwarding. We show that these anomalies are due to the integral nature of VCS, which causes quantization noise in the estimate of connectivity and node location. We propose an aligned virtual coordinate system (AVCS) on which the greedy routing success can be significantly improved. With our approach, and for the first time, we show that greedy routing on VCS outperforms that on physical coordinate systems even in the absence of localization errors. We compare AVCS against some of the most popular geographical routing protocols both on physical coordinate system and the virtual coordinate systems and show that AVCS significantly improves performance over the best known solutions. I.
Abstract Algorithms for ad hoc and sensor networks *
, 2004
"... Wireless and mobiles networks are excellent playground for researchers with an algorithm background. Many research problem turn out to be variants of classic graph theory problems. In particular the rapidly growing areas for ad hoc and sensor networks demand new solutions for timeless graph theory p ..."
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Wireless and mobiles networks are excellent playground for researchers with an algorithm background. Many research problem turn out to be variants of classic graph theory problems. In particular the rapidly growing areas for ad hoc and sensor networks demand new solutions for timeless graph theory problems, because: (i) wireless devices have lower bandwidth and (ii) wireless devices are mobile and therefore the topology of the network changes rather frequently. As a consequences, algorithms for wireless and mobile networks should have: (i) as little communication as possible and should (ii) run as fast as possible. Both goals can only be achieved by developing algorithms requiring a small number of communication rounds only (socalled local algorithm). In the work we present a few algorithmic applications in wireless networking, such as clustering, topology control and georouting. Each section is supplemented with an open problem. q 2005 Elsevier B.V. All rights reserved.
SpiderBat: Augmenting Wireless Sensor Networks with Distance and Angle Information
, 2011
"... Having access to accurate position information is a key requirement for many wireless sensor network applications. We present the design, implementation and evaluation of SpiderBat, an ultrasoundbased ranging platform designed to augment existing sensor nodes with distance and angle information. Sp ..."
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Having access to accurate position information is a key requirement for many wireless sensor network applications. We present the design, implementation and evaluation of SpiderBat, an ultrasoundbased ranging platform designed to augment existing sensor nodes with distance and angle information. SpiderBat features independently controllable ultrasound transmitters and receivers, in all directions of the compass. Using a digital compass, nodes can learn about their orientation, and combine this information with distance and angle measurements using ultrasound. To the best of our knowledge, SpiderBat is the first ultrasoundbased sensor node platform that can measure absolute angles between sensor nodes accurately. The availability of angle information enables us to estimate node positions with a precision in the order of a few centimeters. Moreover, our system allows to position nodes in multihop networks where pure distancebased algorithms must fail, in particular in sparse networks, with only a single anchor node. Furthermore, information on absolute node orientations makes it possible to detect whether two nodes are in lineofsight. Consequently, we can detect the presence of obstacles and walls by looking at patterns in the received ultrasound signal.
Geometric routing without geometry
 in 12th Colloquium on Structural Information and Communication Complexity. MontStMichel
, 2005
"... In this paper we propose a new routing paradigm, called pseudogeometric routing. In pseudogeometric routing, each node u of a network of computing elements is assigned a pseudo coordinate composed of the graph (hop) distances from u to a set of designated nodes (the anchors) in the network. On the ..."
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In this paper we propose a new routing paradigm, called pseudogeometric routing. In pseudogeometric routing, each node u of a network of computing elements is assigned a pseudo coordinate composed of the graph (hop) distances from u to a set of designated nodes (the anchors) in the network. On theses pseudo coordinates we employ greedy geometric routing. Almost as a side effect, pseudogeometric routing is not restricted to planar unit disk graph networks anymore, but succeeds on general networks. 1
Trailing Mobile Sinks: A Proactive Data Reporting Protocol for Wireless Sensor Networks
 In: Proc. of MASS, 2010. 16 Xinxin Liu, Li Yu, Di Wang, and Xiaolin Li
"... using mobile sinks typically incurs constant propagation of sink location indication messages to guide the direction of data reporting. Such behavior is undesirable, especially when the sensor network scale increases, as frequent message flooding will cause serious congestion in network communicati ..."
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using mobile sinks typically incurs constant propagation of sink location indication messages to guide the direction of data reporting. Such behavior is undesirable, especially when the sensor network scale increases, as frequent message flooding will cause serious congestion in network communication and significantly impair the sensor network lifetime. In this paper, we propose a proactive data reporting protocol, SinkTrail, which achieves energy efficient data forwarding to multiple mobile sinks, and effectively reduces the number of sink location broadcasting messages. SinkTrail is unique in two aspects: (1) it allows sufficient flexibility in the movement of mobile sinks to dynamically adapt to unknown terrestrial changes; and (2) without assistance of GPS or predefined landmarks, SinkTrail establishes a logical coordinate system for predicting and tracking mobile sinks’ locations, thereby significantly saves energy consumed during the data reporting process. We systematically analyze the impact of several design factors in SinkTrail and explore potential design improvements. The simulation results demonstrate that SinkTrail outperforms the Frequent Flooding Method (FFM) in finding shorter routing path and consumes 33:8 % less energy at best. I.
Robust georouting on embeddings of dynamic wireless networks
 IN INFOCOM
, 2007
"... Wireless routing based on an embedding of the connectivity graph is a very promising technique to overcome shortcomings of geographic routing and topologybased routing. This is of particular interest when either absolute coordinates for geographic routing are unavailable or when they poorly reflec ..."
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Wireless routing based on an embedding of the connectivity graph is a very promising technique to overcome shortcomings of geographic routing and topologybased routing. This is of particular interest when either absolute coordinates for geographic routing are unavailable or when they poorly reflect the underlying connectivity in the network. We focus on dynamic networks induced by timevarying fading and mobility. This requires that the embedding is stable over time, whereas the focus of most existing embedding algorithms is on low distortion of single realizations of a graph. We develop a beaconbased distributed embedding algorithm that requires little control overhead, produces low distortion embeddings, and is stable. We also show that a lowdimensional embedding suffices, since at a sufficiently large scale, wireless connectivity graphs are dictated by geometry. The stability of the embedding allows us to combine georouting on the embedding with last encounter routing (LER) for node lookup, further reducing the control overhead. Our routing algorithm avoids dead ends through randomized greedy forwarding. We demonstrate through extensive simulations that our combined embedding and routing scheme outperforms existing algorithms.
WGrid: a CrossLayer Infrastructure for MultiDimensional Indexing, Querying and Routing
 in Wireless Ad Hoc and Sensor Networks”, Proc. IEEE Conf. on PeertoPeer Computing
, 2006
"... AbstractLarge scale wireless adhoc networks of computers, sensors, PDAs etc. (i.e. nodes) are revolutionizing connectivity and leading to a paradigm shift from centralized systems to highly distributed and dynamic environments. A plethora of routing algorithms have been proposed for the network p ..."
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AbstractLarge scale wireless adhoc networks of computers, sensors, PDAs etc. (i.e. nodes) are revolutionizing connectivity and leading to a paradigm shift from centralized systems to highly distributed and dynamic environments. A plethora of routing algorithms have been proposed for the network path discovery ranging from broadcasting/floodingbased approaches to those using global positioning systems (GPS). In this paper we propose a novel decentralized infrastructure that selforganizes wireless devices in an adhoc network, where each node has one or more virtual coordinates through which both message routing and data management occur without reliance on either flooding/broadcasting operations or GPS. The resulting adhoc network does not suffer from the deadend problem, which happens in geographicbased routing when a node is unable to locate a neighbor closer to the destination than itself. The multidimensional data management capability will be described showing, as an example, how the location service reduces to a simple query, like for any other data type. Extensive performance analysis and experiments have been conducted and the results compared to GPSR, which is considered the most efficient routing solution not using broadcast operations. Our approach shows significant performance gains.
Robust topology control protocols
 IN: PROC. OF THE 8 TH INTERNATIONAL CONFERENCE ON PRINCIPLES OF DISTRIBUTED SYSTEMS (OPODIS
, 2005
"... Topology control protocols attempt to reduce the energy consumption of nodes in an adhoc wireless network while maintaining sufficient network connectivity. Topology control protocols with various features have been proposed, but they all lack robustness and are extremely sensitive to faulty info ..."
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Topology control protocols attempt to reduce the energy consumption of nodes in an adhoc wireless network while maintaining sufficient network connectivity. Topology control protocols with various features have been proposed, but they all lack robustness and are extremely sensitive to faulty information from neighbors. For example, the XTC protocol (R. Wattenhofer and A. Zollinger, XTC: A practical topology control algorithm for adhoc networks, WMAN 2004) canbeforced to construct a disconnected network even if two nodes in the network receive slightly faulty distance information from one neighbor each. A key step in most localized topology control protocols is one in which each node establishes a total ordering on its set of neighbors based on information received from them. In this paper, we propose a metric for robustness of localized topology control protocols and define an rrobust topology control protocol as one that returns a correct output network even when its neighborhood orderings have been modified by up to r − 1 adjacent swaps by a malicious adversary. We then modify XTC in a simple manner to derive a family of rrobust protocols for any r>1. The price we pay for increased robustness is in terms of decreased network sparsity; however we can bound this decrease and we show that in transforming XTC from a 1robust protocol (which it trivially is) into an rrobust protocol, the maximum vertex degree of the output network increases by a factor of O ( √ r). An extremely pleasant sideeffect of our design is that the output network is both Ω ( √ r)edge connected and Ω ( √ r)vertex connected provided the input network is. Thus ensuring robustness of the protocol seems to give faulttolerance of the output for free. Our rrobust version of XTC is almost as simple and practical as XTC and like XTC it only involves 2 rounds of communication between a node and its neighbors.