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77
Geometric Spanner for Routing in Mobile Networks
, 2001
"... Abstract—We propose a new routing graph, the restricted Delaunay graph (RDG), for mobile ad hoc networks. Combined with a node clustering algorithm, the RDG can be used as an underlying graph for geographic routing protocols. This graph has the following attractive properties: 1) it is planar; 2) be ..."
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Cited by 167 (19 self)
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Abstract—We propose a new routing graph, the restricted Delaunay graph (RDG), for mobile ad hoc networks. Combined with a node clustering algorithm, the RDG can be used as an underlying graph for geographic routing protocols. This graph has the following attractive properties: 1) it is planar; 2) between any two graph nodes there exists a path whose length, whether measured in terms of topological or Euclidean distance, is only a constant times the minimum length possible; and 3) the graph can be maintained efficiently in a distributed manner when the nodes move around. Furthermore, each node only needs constant time to make routing decisions. We show by simulation that the RDG outperforms previously proposed routing graphs in the context of the Greedy perimeter stateless routing (GPSR) protocol. Finally, we investigate theoretical bounds on the quality of paths discovered using GPSR. Index Terms—Geographical routing, spanners, wireless ad hoc networks. I.
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 52 (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.
Multicast capacity for large scale wireless ad hoc networks
 In ACM Mobicom
, 2007
"... In this paper, we study the capacity of a largescale random wireless network for multicast. Assume that n wireless nodes are randomly deployed in a square region with sidelength a and all nodes have the uniform transmission range r and uniform interference range R> r. We further assume that eac ..."
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Cited by 45 (18 self)
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In this paper, we study the capacity of a largescale random wireless network for multicast. Assume that n wireless nodes are randomly deployed in a square region with sidelength a and all nodes have the uniform transmission range r and uniform interference range R> r. We further assume that each wireless node can transmit/receive at W bits/second over a common wireless channel. For each node vi, we randomly pick k − 1 nodes from the other n − 1 nodes as the receivers of the multicast session rooted at node vi. The aggregated multicast capacity is defined as the total data rate of all multicast sessions in the network. In this paper we derive matching asymptotic upper bounds and lower bounds on multicast capacity of random wireless networks. We show that the total multicast capacity is Θ( � n log n · W √ k) when k = O ( n log n
On connected multiple point coverage in wireless sensor networks
 Journal of Wireless Information Networks
, 2006
"... Abstract — We consider a wireless sensor network consisting of a set of sensors deployed randomly. A point in the monitored area is covered if it is within the sensing range of a sensor. In some applications, when the network is sufficiently dense, area coverage can be approximated by guaranteeing ..."
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Cited by 26 (0 self)
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Abstract — We consider a wireless sensor network consisting of a set of sensors deployed randomly. A point in the monitored area is covered if it is within the sensing range of a sensor. In some applications, when the network is sufficiently dense, area coverage can be approximated by guaranteeing point coverage. In this case, all the points of wireless devices could be used to represent the whole area, and the working sensors are supposed to cover all the sensors. Many applications related to security and reliability require guaranteed kcoverage of the area at all times. In this paper, we formalize the k(Connected) Coverage Set (kCCS/kCS) problems, develop a linear programming algorithm, and design two nonglobal solutions for them. Some theoretical analysis is also provided followed by simulation results. Index Terms — Coverage problem, linear programming, localized algorithms, reliability, wireless sensor networks.
Extended Multipoint Relays to Determine Connected Dominating Sets in MANETs
 IEEE Transactions on Computers
, 2006
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Minimum power configuration for wireless communication in sensor networks
 JOURNAL PUBLICATIONS AND 18 PAPERS PRESENTED IN INTERNATIONAL CONFERENCES. HIS
, 2007
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Extended Dominating Set and Its Applications in Ad Hoc Networks Using Cooperative Communication
 IEEE TRANS. PARALLEL AND DISTRIBUTED SYSTEMS, ACCEPTED FOR PUBLICATION
, 2005
"... We propose a notion of extended dominating set where each node in an ad hoc network is covered by either a dominating neighbor or several 2hop dominating neighbors. This work is motivated by cooperative communication in ad hoc networks whereby transmitting independent copies of a packet generates d ..."
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Cited by 13 (2 self)
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We propose a notion of extended dominating set where each node in an ad hoc network is covered by either a dominating neighbor or several 2hop dominating neighbors. This work is motivated by cooperative communication in ad hoc networks whereby transmitting independent copies of a packet generates diversity and combats the effects of fading. We first show the NPcompleteness of the minimum extended dominating set problem. Then, several heuristic algorithms, global and local, for constructing a small extended dominating set are proposed. These are nontrivial extensions of the existing algorithms for the regular dominating set problem. The application of the extended dominating set in efficient broadcasting is also discussed. The performance analysis includes an analytical study in terms of approximation ratio and a simulation study of the average size of the extended dominating set derived from the proposed algorithms.
Local solutions for global problems in wireless networks
 Journal of Discrete Algorithms
, 2007
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Sparse geometric graphs with small dilation. Computational Geometry: Theory and Application. Article in press. doi:10.1016/j.comgeo.2007.07.004
"... Given a set S of n points in R D, and an integer k such that 0 � k < n, we show that a geometric graph with vertex set S, at most n − 1 + k edges, maximum degree five, and dilation O(n/(k + 1)) can be computed in time O(n log n). For any k, we also construct planar npoint sets for which any geom ..."
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Cited by 11 (5 self)
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Given a set S of n points in R D, and an integer k such that 0 � k < n, we show that a geometric graph with vertex set S, at most n − 1 + k edges, maximum degree five, and dilation O(n/(k + 1)) can be computed in time O(n log n). For any k, we also construct planar npoint sets for which any geometric graph with n − 1 + k edges has dilation Ω(n/(k + 1)); a slightly weaker statement holds if the points of S are required to be in convex position. 1 Preliminaries and introduction A geometric network is an undirected graph whose vertices are points in R D. Geometric networks, especially geometric networks of points in the plane, arise in many applications. Road networks, railway networks, computer networks—any collection of objects that have some connections between them can be modeled as a geometric network. A natural and widely studied type of geometric network is the Euclidean network, where the weight of an edge is simply the Euclidean distance between its two endpoints. Such networks for points in R D form the topic of study of our paper. When designing a network for a given set S of points, several criteria have to be taken into account. In particular, in many applications it is important to ensure a short connection between every two points in S.
Finding the best shortcut in a geometric network
 ACM Symp. Comput. Geom
, 2005
"... Given a Euclidean graph G in R d with n vertices and m edges we consider the problem of adding a shortcut such that the stretch factor of the resulting graph is minimized. Currently, the fastest algorithm for computing the stretch factor of a Euclidean graph runs in O(mn + n 2 log n) time, resulting ..."
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Cited by 8 (2 self)
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Given a Euclidean graph G in R d with n vertices and m edges we consider the problem of adding a shortcut such that the stretch factor of the resulting graph is minimized. Currently, the fastest algorithm for computing the stretch factor of a Euclidean graph runs in O(mn + n 2 log n) time, resulting in a trivial O(mn 3 + n 4 log n) time algorithm for computing the optimal shortcut. First, we show that a simple modification yields the optimal solution in O(n 4) time using O(n 2) space. To reduce the running times we consider several approximation algorithms. Our main result is a (2 + ε)approximation algorithm with running time O(nm + n 2 (log n +1/ε 3d)) using O(n 2)space.