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122
Geometric AdHoc Routing: Of Theory and Practice
, 2003
"... All too often a seemingly insurmountable divide between theory and practice can be witnessed. In this paper we try to contribute to narrowing this gap in the field of adhoc routing. In particular we consider two aspects: We propose a new geometric routing algorithm which is outstandingly e#cient on ..."
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Cited by 304 (13 self)
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All too often a seemingly insurmountable divide between theory and practice can be witnessed. In this paper we try to contribute to narrowing this gap in the field of adhoc routing. In particular we consider two aspects: We propose a new geometric routing algorithm which is outstandingly e#cient on practical averagecase networks, however is also in theory asymptotically worstcase optimal. On the other hand we are able to drop the formerly necessary assumption that the distance between network nodes may not fall below a constant value, an assumption that cannot be maintained for practical networks. Abandoning this assumption we identify from a theoretical point of view two fundamentamentally di#erent classes of cost metrics for routing in adhoc networks.
Discrete Mobile Centers
 Discrete and Computational Geometry
, 2001
"... We propose a new randomized algorithm for maintaining a set of clusters among moving nodes in the plane. Given a specified cluster radius, our algorithm selects and maintains a variable subset of the nodes as cluster centers. This subset has the property that (1) balls of the given radius centered a ..."
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Cited by 101 (15 self)
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We propose a new randomized algorithm for maintaining a set of clusters among moving nodes in the plane. Given a specified cluster radius, our algorithm selects and maintains a variable subset of the nodes as cluster centers. This subset has the property that (1) balls of the given radius centered at the chosen nodes cover all the others and (2) the number of centers selected is a constantfactor approximation of the minimum possible. As the nodes move, an eventbased kinetic data structure updates the clustering as necessary. This kinetic data structure is shown to be responsive, efficient, local, and compact. The produced cover is also smooth, in the sense that wholesale cluster rearrangements are avoided. The algorithm can be implemented without exact knowledge of the node positions, if each node is able to sense its distance to other nodes up to the cluster radius. Such a kinetic clustering can be used in numerous applications where mobile devices must be interconnected into an adhoc network to collaboratively perform some tasks. 1
PolynomialTime Approximation Schemes for Geometric Graphs
, 2001
"... A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present polynomialtime approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total weigh ..."
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Cited by 97 (5 self)
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A disk graph is the intersection graph of a set of disks with arbitrary diameters in the plane. For the case that the disk representation is given, we present polynomialtime approximation schemes (PTASs) for the maximum weight independent set problem (selecting disjoint disks of maximum total weight) and for the minimum weight vertex cover problem in disk graphs. These are the first known PTASs for NPhard optimization problems on disk graphs. They are based on a novel recursive subdivision of the plane that allows applying a shifting strategy on different levels simultaneously, so that a dynamic programming approach becomes feasible. The PTASs for disk graphs represent a common generalization of previous results for planar graphs and unit disk graphs. They can be extended to intersections graphs of other "disklike" geometric objects (such as squares or regular polygons), also in higher dimensions.
Robust PositionBased Routing in Wireless Ad Hoc Networks with Unstable Transmission Ranges (Extended Abstract)
"... Several papers showed how to perform routing in ad hoc wireless networks based on the positions of the mobile hosts. However, all these protocols are likely to fail if the transmission ranges of the mobile hosts vary due to natural or manmade obstacles or weather conditions. These protocols may fai ..."
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Cited by 89 (4 self)
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Several papers showed how to perform routing in ad hoc wireless networks based on the positions of the mobile hosts. However, all these protocols are likely to fail if the transmission ranges of the mobile hosts vary due to natural or manmade obstacles or weather conditions. These protocols may fail because in routing either some connections are not considered which eectively results in disconnecting the network, or the use of some connections causes livelocks. In this paper, we describe a robust routing protocol that tolerates up to roughly 40% of variation in the transmission ranges of the mobile hosts. More precisely, our protocol guarantees message delivery in a connected adhoc network whenever the ratio of the maximum transmission range to the minimum transmission range is at most 2.
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 74 (1 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.
A generic distributed broadcast scheme in ad hoc wireless networks
 IEEE Transactions on Computers
, 2004
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Initializing Newly Deployed Ad Hoc and Sensor Networks
 in Proceedings of 10 th Annual International Conference on Mobile Computing and Networking (MOBICOM
, 2004
"... A newly deployed multihop radio network is unstructured and lacks a reliable and e#cient communication scheme. In this paper, we take a step towards analyzing the problems existing during the initialization phase of ad hoc and sensor networks. Particularly, we model the network as a multihop quasi ..."
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Cited by 58 (15 self)
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A newly deployed multihop radio network is unstructured and lacks a reliable and e#cient communication scheme. In this paper, we take a step towards analyzing the problems existing during the initialization phase of ad hoc and sensor networks. Particularly, we model the network as a multihop quasi unit disk graph and allow nodes to wake up asynchronously at any time. Further, nodes do not feature a reliable collision detection mechanism, and they have only limited knowledge about the network topology. We show that even for this restricted model, a good clustering can be computed e#ciently. Our algorithm e#ciently computes an asymptotically optimal clustering. Based on this algorithm, we describe a protocol for quickly establishing synchronized sleep and listen schedule between nodes within a cluster. Additionally, we provide simulation results in a variety of settings.
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 54 (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).
Efficient distributed lowcost backbone formation for wireless networks
 IEEE Transactions on Parallel and Distributed Systems
, 2006
"... Backbone has been used extensively in various aspects (e.g., routing, route maintenance, broadcast, scheduling) for wireless networks. Previous methods are mostly designed to minimize the backbone size. However, in many applications, it is desirable to construct a backbone with small cost when eac ..."
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Cited by 49 (8 self)
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Backbone has been used extensively in various aspects (e.g., routing, route maintenance, broadcast, scheduling) for wireless networks. Previous methods are mostly designed to minimize the backbone size. However, in many applications, it is desirable to construct a backbone with small cost when each wireless node has a cost of being in the backbone. In this paper, we first show that previous methods specifically designed to minimize the backbone size may produce a backbone with a large cost. We then propose an efficient distributed method to construct a weighted sparse backbone with low cost. We prove that the total cost of the constructed backbone is within a small constant factor of the optimum for homogeneous networks when either the nodes ’ costs are smooth or the network maximum node degree is bounded. We also show that with a small modification the constructed backbone is efficient for unicast: the total cost (or hop) of the least cost (or hop) path connecting any two nodes using backbone is no more than 3 (or 4) times of the least cost (or hop) path in the original communication graph. As a side product, we give an efficient overlay based multicast structure whose total cost is no more than 10 times of the minimum when the network is modeled by UDG. Our theoretical results are corroborated by our simulation studies.
PolynomialTime Approximation Schemes for Packing and Piercing Fat Objects
 Journal of Algorithms
, 2001
"... We consider two problems: given a collection of n fat objects in a xed dimension, 1. (packing) nd the maximum subcollection of pairwise disjoint objects, and 2. (piercing) nd the minimum point set that intersects every object. Recently, Erlebach, Jansen, and Seidel gave a polynomialtime approxim ..."
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Cited by 44 (6 self)
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We consider two problems: given a collection of n fat objects in a xed dimension, 1. (packing) nd the maximum subcollection of pairwise disjoint objects, and 2. (piercing) nd the minimum point set that intersects every object. Recently, Erlebach, Jansen, and Seidel gave a polynomialtime approximation scheme (PTAS) for the packing problem, based on a shifted hierarchical subdivision method. Using shifted quadtrees, we describe a similar algorithm for packing but with a smaller time bound. Erlebach et al.'s algorithm requires polynomial space. We describe a dierent algorithm, based on geometric separators, that requires only linear space. This algorithm can also be applied to piercing, yielding the rst PTAS for that problem. Abbreviated title. Packing and Piercing Fat Objects. Keywords. Computational geometry, approximation algorithms, maximum independent set, hitting set, quadtrees, dynamic programming, separator theorems. 1