J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu, "Discrete Mobile Centers," in Proceedings of the 17 annual symposium on Computational geometry (SCG). ACM Press, 2001, pp. 188--196.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and maintain the 1 center and the 1 median for a given set of n moving points on the plane (1 median is de ned as a point which minimizes the sum of all distances to the input points) which gives an algorithm to select clusterheads if mobiles are already partitioned into clusters. Gao et al. [14] proposed a randomized algorithm for maintaining a set of clusters among moving points on the plane. They [14] presented algorithms with expected approximation factor (on the optimal number of centers) of c log n for intervals and of c n log n for squares . The probability that there are ....

....ned as a point which minimizes the sum of all distances to the input points) which gives an algorithm to select clusterheads if mobiles are already partitioned into clusters. Gao et al. 14] proposed a randomized algorithm for maintaining a set of clusters among moving points on the plane. They [14] presented algorithms with expected approximation factor (on the optimal number of centers) of c log n for intervals and of c n log n for squares . The probability that there are more than the expected number of centers is O(1=n (c ) for the case of intervals and O(1=n c log n ) ....

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J. Gao, L. J. Guibas, J. Hershburger, L. Zhang, and A. Zhu. Discrete mobile centers. In 17th ACM Symposium on Computational Geometry, Boston, MA., jun 2001. To appear.

....and maintain the one center and the one median for a given set of n moving points on the plane (the one median is a point that minimizes the sum of all distances to the input points) Their algorithm can be used to select clusterheads if mobiles are already partitioned into clusters. Gao et al. [14] proposed a randomized algorithm for maintaining a set of clusters based on geometric centers, for a xed radius, among moving points on the plane. Their algorithms have expected approximation factor on the optimal number of centers (or, equivalently, of clusters) of c 1 log n for intervals and of ....

....the optimal number of centers is 1=n for the case of intervals; for squares, the probability that there are more than c n ln n times the optimal number of centers is 1=n ) ln n , for constant c. An extension of this basic algorithm led to a hierarchical algorithm, also presented in [14], based on kinetic data structures [5] The hierarchical algorithm admits an expected constant approximation factor on the number of discrete centers, where the approximation factor also depends linearly on the constants c 1 and c 2 . The dependency of the approximation factor and the probability ....

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J. Gao, L. J. Guibas, J. Hershburger, L. Zhang, and A. Zhu. Discrete mobile centers. In Proc. 17th ACM Sympos. on Computational Geometry, pages 188-196, 2001.

....that is, di#ering by multiplicative and or additive constants only. Unless stated otherwise, we simply refer to the cost of an edge and mean any cost metric belonging to the above class of cost functions. Using clustering techniques a similar result can be achieved without the#1012 del [1, 9, 18]. We will however adhere to this model for simplicity. By the cost of a path we denote the sum of all costs of the edges on the path. The cost of an algorithm is the total cost expended for all messages sent during the algorithm execution (the considered algorithms do not send messages in ....

J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete mobile centers. In Proc. 17th annual symposium on Computational geometry (SCG, pages 188--196. ACM Press, 2001.

....respectively. In polylogarithmic time they both achieve a (1 #) approximation for the linear program. For ad hoc networks, the (connected) dominating set problem has also been studied for special graphs. In particular for the unit disk graph a number of publications have been written (e.g. [1, 7]) For the unit disk graph the problem is known to remain NPhard; however, constant factor approximations are possible in this case. For a recent survey on ad hoc routing and related problems, we refer to [17] 3 Notation and Preliminaries In this section we introduce notations as well as some ....

J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. of the 17th annual symposium on Computational geometry (SCG), pages 188--196. ACM Press, 2001.

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. 17 Annual Symposium on Computational Geometry (SCG), pages 188--196. ACM Press, 2001.

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Jie Gao, Leonidas J. Guibas, John Hershberger, Li Zhang, and An Zhu, "Discrete mobile centers," Discrete and Computational Geometry, vol. 30, no. 1, pp. 45--65, 2003.

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete mobile centers. Discrete Comput. Geom., 30(1):45-63, 2003.

....that a) GBG is a bounded degree unit disk graph and b) the nodes of GBG form a connected dominating set of G. Consequently, all nodes of G have at least one neighbor in GBG . The distributed construction of a subgraph of G with properties a) and b) is described in a number of publications (e.g. [1, 9, 25]) As the backbone contains a dominating set of the underlying graph, every regular node (a node not in the backbone) can be associated to one of its dominators. Since this can be regarded as a clustering of all regular nodes around their dominators, we call this graph the Clustered Backbone ....

J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. 17 Annual Symposium on Computational Geometry (SCG), pages 188--196. ACM Press, 2001.

....on their current locations and a certain desired cluster radius (perhaps corresponding to a radio link range) see Figure 5. The cluster organization will allow for simpler communication protocols among vehicles in the same cluster, and avoid duplicate sensor measurements by nearby vehicles. In [17] we gave a distributed randomized algorithm that performs this type of cluster formation and yields a number of clusters that is a constant fraction approximation of the optimum possible, with high probability. The algorithm is based on a cluster head nomination protocol. We assume that ....

.... the vehicle of highest UID that is within its radius (this might be itself) All nominated vehicles become cluster heads and form a cluster with all their nominators (except for those that they themselves became cluster heads) This extremely simple protocol does not quite work, but as shown in [17], a very simple hierarchical variant of the same algorithm does. In the hierarchical version we use repeatedly the cluster nomination procedure with geometrically increasing radii, up to the final desired radius. At each round only the leaders already elected in the previous round participate. ....

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete mobile centers. In ACM Symposium on Computational Geometry (SoCG '01), 2001.

....v, u first forwards the packet to its clusterhead, and the packet is then forwarded among clusterheads and gateways until it reaches some clusterhead or gateway that is visible to v. We use a clustering algorithm to guarantee that each clusterhead gateway has only a constant number of neighbors [11]. This simplifies forwarding during routing. In [13] the greedy geographic forwarding is done by examining all the neighboring nodes in order to skip short edges in the graph. This process is expensive when the nodes are densely distributed. In our routing graph, since we cluster nodes in the ....

....the quality of the subgraph. One of the major goals of this paper is to construct a subgraph G with constant stretch factor. This graph G can serve as a routing graph in the ad hoc network. Our construction consists of two phases. First, we make use of the hierarchical clustering algorithm in [11] to select a small subset of V , called clusterheads, so that each node in V can communicate directly to some clusterheads. Each non clusterhead node in V (called a client) is assigned to a unique clusterhead visible to it. We also identify those pairs of clusterheads that may communicate to each ....

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J. Gao, L. J. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete mobile centers. In Proc. 17th ACM Symp. on Computational Geometry, Jun 2001.

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu, "Discrete Mobile Centers," in Proceedings of the 17 annual symposium on Computational geometry (SCG). ACM Press, 2001, pp. 188--196.

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. 17 Annual Symposium on Computational Geometry (SCG), pages 188--196. ACM Press, 2001.

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. 17 Symposium on Computational Geometry (SCG), pages 188--196. ACM Press, 2001.

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. 17 Annual Symposium on Computational Geometry (SCG), pages 188--196. ACM Press, 2001.

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. 17 Symposium on Computational Geometry (SCG), pages 188--196, 2001.

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. of the 17th annual symposium on Computational geometry (SCG), pages 188--196. ACM Press, 2001.

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. 17 Symposium on Computational Geometry (SCG), pages 188--196. ACM Press, 2001.

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. 17 Symposium on Computational Geometry (SCG), pages 188--196, 2001.

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. 17 Annual Symposium on Computational Geometry (SCG), pages 188--196. ACM Press, 2001.

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J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete mobile centers. In Proc. 17th Annu. ACM Sympos. Comput. Geom., pages 188-196, 2001.

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J. Gao, L. J. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. of the 17th Symposium on Computational Geometry (SOCG'01), pages 188--196, 2001.

No context found.

J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. 17 Annual Symposium on Computational Geometry (SCG), pages 188--196. ACM Press, 2001.

No context found.

J. Gao, L. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. of the 17 annual symposium on Computational geometry (SCG), pages 188--196. ACM Press, 2001.

No context found.

J. Gao, L. J. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete Mobile Centers. In Proc. of the 17th Symposium on Computational Geometry (SOCG'01), pages 188--196, 2001.

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J. Gao, L. J. Guibas, J. Hershberger, L. Zhang, and A. Zhu. Discrete mobile centers. In Proc. Symposium on Computational Geometry, pages 188--196, Medford, MA, USA, 2001.

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