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238
2004a). Robust rendezvous for mobile autonomous agents via proximity graphs in d dimensions
 IEEE Transactions on Automatic Control. Submitted. Electronic
"... Abstract: This paper presents coordination algorithms for networks of mobile autonomous agents. The objective of the proposed algorithms is to achieve rendezvous, that is, agreement over the location of the agents in the network. We provide analysis and design results for multiagent networks in arb ..."
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Cited by 202 (22 self)
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Abstract: This paper presents coordination algorithms for networks of mobile autonomous agents. The objective of the proposed algorithms is to achieve rendezvous, that is, agreement over the location of the agents in the network. We provide analysis and design results for multiagent networks in arbitrary dimensions under weak requirements on the switching and failing communication topology. The correctness proof relies on proximity graphs and their properties and on a LaSalle Invariance Principle for nondeterministic discretetime systems. Copyright c ○ 2005 IFAC
Analysis of a conebased distributed topology control algorithm for wireless multihop networks
 In ACM Symposium on Principle of Distributed Computing (PODC
, 2001
"... bahl~microsoft, corn ymwang~microsoft, corn rogerwa~microsoft, corn The topology of a wireless multihop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a conebased distributed topology control algorithm. This algorithm, intr ..."
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Cited by 183 (18 self)
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bahl~microsoft, corn ymwang~microsoft, corn rogerwa~microsoft, corn The topology of a wireless multihop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a conebased distributed topology control algorithm. This algorithm, introduced in [16], does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node u transmits with the minimum power P~,,a required to ensure that in every cone of degree a around u, there is some node that u can reach with power Pma We show that taking a = 57r/6 is a necessary and sufficient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from a to t when every node communicates at maximum power then, if a < _ 5~r/6, there is still a path in the smallest symmetric graph Ga containing all edges (u, v) such that u can communicate with v using power p~,a. On the other hand, if ~> 51r/6, connectivity is not necessarily preserved. We also propose a set of optimizations that further reduce power consumption and prove that they retain network connectivity. Dynamic reconfiguration in the presence of failures and mobility is also discussed. Simulation results are presented to demonstrate the effectiveness of the algorithm and the optimizations. 1.
Coverage in Wireless Adhoc Sensor Networks
, 2002
"... Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking [1]. One of the fundamental problems in sensor networks is the calculation of the coverage. In [1], it is assumed that the sensor has the uniform sensing ability. In this pape ..."
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Cited by 165 (11 self)
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Sensor networks pose a number of challenging conceptual and optimization problems such as location, deployment, and tracking [1]. One of the fundamental problems in sensor networks is the calculation of the coverage. In [1], it is assumed that the sensor has the uniform sensing ability. In this paper, we give efficient distributed algorithms to optimally solve the bestcoverage problem raised in [1]. Here, we consider the sensing model: the sensing ability diminishes as the distance increases. As energy conservation is a major concern in wireless (or sensor) networks, we also consider how to find an optimum bestcoverage path with the least energy consumption. We also consider how to find an optimum bestcoveragepath that travels a small distance. In addition, we justify the correctness of the method proposed in [1] that uses the Delaunay triangulation to solve the best coverage problem. Moreover, we show that the search space of the best coverage problem can be confined to the relative neighborhood graph, which can be constructed locally.
Automatic Rigging and Animation of 3D Characters
 ACM Transactions on Graphics (SIGGRAPH proceedings
"... Copyright Notice ..."
Spatiallydistributed coverage optimization and control with limitedrange interactions
 ESAIM Control, Optimisation Calculus Variations
, 2005
"... Abstract. This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the geometry of Voronoi partitions and proximity grap ..."
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Cited by 95 (30 self)
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Abstract. This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the geometry of Voronoi partitions and proximity graphs, we analyze a class of aggregate objective functions and propose coverage algorithms in continuous and discrete time. These algorithms have convergence guarantees and are spatially distributed with respect to appropriate proximity graphs. Numerical simulations illustrate the results.
A ConeBased Distributed TopologyControl Algorithm for Wireless MultiHop Networks
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 2002
"... The topology of a wireless multihop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a conebased distributed topology control algorithm. This algorithm does not assume that nodes have GPS information available; rather it dep ..."
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Cited by 62 (1 self)
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The topology of a wireless multihop network can be controlled by varying the transmission power at each node. In this paper, we give a detailed analysis of a conebased distributed topology control algorithm. This algorithm does not assume that nodes have GPS information available; rather it depends only on directional information. Roughly speaking, the basic idea of the algorithm is that a node u transmits with the minimum power p u,# required to ensure that in every cone of degree # around u, there is some node that u can reach with power p u,# . We show that taking # = 5#/6 is a necessary and sufficient condition to guarantee that network connectivity is preserved. More precisely, if there is a path from s to t when every node communicates at maximum power then, if # 5#/6, there is still a path in the smallest symmetric graph G # containing all edges (u, v) such that u can communicate with v using power p u,# . On the other hand, if # > 5#/6,
Finitetime convergent gradient flows with applications to network consensus
 Automatica
"... This paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function. Extending recent results on nonsmooth stability analysis, we characterize their asymptotic convergence properties and identify conditions that guarantee finitetime convergence. We d ..."
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Cited by 62 (5 self)
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This paper introduces the normalized and signed gradient dynamical systems associated with a differentiable function. Extending recent results on nonsmooth stability analysis, we characterize their asymptotic convergence properties and identify conditions that guarantee finitetime convergence. We discuss the application of the results to the design of multiagent coordination algorithms, paying special attention to their scalability properties. Finally, we consider network consensus problems and show how the proposed nonsmooth gradient flows achieve the desired coordination task in finite time.
Graphtheoretic scagnostics
 In Proc. 2005 IEEE Symp. on Information Visualization (INFOVIS
, 2005
"... We introduce Tukey and Tukey scagnostics and develop graphtheoretic methods for implementing their procedure on large datasets. ..."
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Cited by 54 (1 self)
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We introduce Tukey and Tukey scagnostics and develop graphtheoretic methods for implementing their procedure on large datasets.
Shapes And Implementations In ThreeDimensional Geometry
, 1993
"... Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is often useful or required to compute what one might call the "shape" of the set. For that purpose, this thesis deals with the formal notion of the family of alpha shapes of a finite point ..."
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Cited by 39 (5 self)
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Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is often useful or required to compute what one might call the "shape" of the set. For that purpose, this thesis deals with the formal notion of the family of alpha shapes of a finite point set in three dimensional space. Each shape is a welldefined polytope, derived from the Delaunay triangulation of the point set, with a real parameter controlling the desired level of detail. Algorithms and data structures are presented that construct and store the entire family of shapes, with a quadratic time and space complexity, in the worst case.
Modeling and visualization of leaf venation patterns
"... We introduce a class of biologically−motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution ..."
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Cited by 38 (7 self)
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We introduce a class of biologically−motivated algorithms for generating leaf venation patterns. These algorithms simulate the interplay between three processes: (1) development of veins towards hormone (auxin) sources embedded in the leaf blade; (2) modification of the hormone source distribution by the proximity of veins; and (3) modification of both the vein pattern and source distribution by leaf growth. These processes are formulated in terms of iterative geometric operations on sets of points that represent vein nodes and auxin sources. In addition, a vein connection graph is maintained to determine vein widths. The effective implementation of the algorithms relies on the use of space subdivision (Voronoi diagrams) and time coherence between iteration steps. Depending on the specification details and parameters used, the algorithms can simulate many types of venation patterns, both open (tree−like) and closed (with loops). Applications of the presented algorithms include texture and detailed structure generation for image synthesis purposes, and modeling of morphogenetic processes in support of biological research.