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307
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
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Cited by 520 (40 self)
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Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows: ffl We devise a model for dynamic graph algorithms, based on performing queries and updates on an implicit representation of the drawing, and we show its applications. ffl We present several efficient dynamic drawing algorithms for trees, seriesparallel digraphs, planar stdigraphs, and planar graphs. These algorithms adopt a variety of representations (e.g., straightline, polyline, visibility), and update the drawing in a smooth way.
Mobile Sensor Network Deployment using Potential Fields: A Distributed, Scalable Solution to the Area Coverage Problem
, 2002
"... This paper considers the problem of deploying a mobile sensor network in an unknown environment. A mobile sensor network is composed of a distributed collection of nodes, each of which has sensing, computation, communication and locomotion capabilities. Such networks are capable of selfdeployment; ..."
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Cited by 238 (15 self)
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This paper considers the problem of deploying a mobile sensor network in an unknown environment. A mobile sensor network is composed of a distributed collection of nodes, each of which has sensing, computation, communication and locomotion capabilities. Such networks are capable of selfdeployment; i.e., starting from some compact initial configuration, the nodes in the network can spread out such that the area `covered' by the network is maximized. In this paper, we present a potentialfieldbased approach to deployment. The fields are constructed such that each node is repelled by both obstacles and by other nodes, thereby forcing the network to spread itself throughout the environment. The approach is both distributed and scalable.
Grid coverage for surveillance and target location in distributed sensor networks
 IEEE Transactions on Computers
, 2002
"... AbstractWe present novel grid coverage strategies for effective surveillance and target location in distributed sensor networks. We represent the sensor field as a grid (two or threedimensional) of points (coordinates) and use the term target location to refer to the problem of locating a target a ..."
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Cited by 168 (12 self)
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AbstractWe present novel grid coverage strategies for effective surveillance and target location in distributed sensor networks. We represent the sensor field as a grid (two or threedimensional) of points (coordinates) and use the term target location to refer to the problem of locating a target at a grid point at any instant in time. We first present an integer linear programming (ILP) solution for minimizing the cost of sensors for complete coverage of the sensor field. We solve the ILP model using a representative publicdomain solver and present a divideandconquer approach for solving large problem instances. We then use the framework of identifying codes to determine sensor placement for unique target location. We Fig. 1. An examPle of a twodimensional sensor field. provide codingtheoretic bounds on the number of sensors and present methods report a large in their respective zones. The precise location of the for determining their placement in the sensor field. We also show that gridbased target must th n be detern'rined by examining the location of these sensor placement for single targets provides asymptotically (unambiguous) location of multiple targets in the grid. complete sensors. In target (within y cases, it is even impossible to precisely locate the e granularity of a single grid point). Alternatively, target locati can be simplified considerably if the sensors are placed in su a way that every grid point in the sensor field is covered by a unique subset of sensors. In this way, the set of sensors repo g a target at time t uniquely identifies the grid 1
An Incremental SelfDeployment Algorithm for Mobile Sensor Networks
 AUTONOMOUS ROBOTS, SPECIAL ISSUE ON INTELLIGENT EMBEDDED SYSTEMS
, 2001
"... This paper describes an incremental deployment algorithm for mobile sensor networks. A mobile sensor network is a distributed collection of nodes, each of which has sensing, computation, communication and locomotion capabilities. The algorithm deploys nodes oneatatime into an unknown environment, ..."
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Cited by 165 (10 self)
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This paper describes an incremental deployment algorithm for mobile sensor networks. A mobile sensor network is a distributed collection of nodes, each of which has sensing, computation, communication and locomotion capabilities. The algorithm deploys nodes oneatatime into an unknown environment, with each node making use of information gathered by previously deployed nodes to determine its target location. The algorithm is designed to maximize network `coverage' whilst simultaneously ensuring that nodes retain lineofsight with one another (this latter constraint arises from the need to localize the nodes; in our previous work on meshbased localization [12, 13] we have shown how nodes can localize themselves in a completely unknown environment by using other nodes as landmarks). This paper describes the incremental deployment algorithm and presents the results of an extensive series of simulation experiments. These experiments serve to both validate the algorithm and illuminate its empirical properties.
Sensor Deployment and Target Localization Based on Virtual Forces
, 2003
"... The effectiveness of clusterbased distributed sensor networks depends to a large extent on the coverage provided by the sensor deployment. We propose a virtual force algorithm (VFA) as a sensor deployment strategy to enhance the coverage after an initial random placement of sensors. For a given num ..."
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Cited by 149 (3 self)
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The effectiveness of clusterbased distributed sensor networks depends to a large extent on the coverage provided by the sensor deployment. We propose a virtual force algorithm (VFA) as a sensor deployment strategy to enhance the coverage after an initial random placement of sensors. For a given number of sensors, the VFA algorithm attempts to maximize the sensor field coverage. A judicious combination of attractive and repulsive forces is used to determine virtual motion paths and the rate of movement for the randomlyplaced sensors. Once the effective sensor positions are identified, a onetime movement with energy consideration incorporated is carried out, i.e., the sensors are redeployed to these positions. We also propose a novel probabilistic target localization algorithm that is executed by the cluster head. The localization results are used by the cluster head to query only a few sensors (out of those that report the presence of a target) for more detailed information. Simulation results are presented to demonstrate the effectiveness of the proposed approach.
A survey of visibility for walkthrough applications
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER
, 2003
"... Visibility algorithms for walkthrough and related applications have grown into a significant area, spurred by the growth in the complexity of models and the need for highly interactive ways of navigating them. In this survey, we review the fundamental issues in visibility and conduct an overview of ..."
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Cited by 145 (8 self)
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Visibility algorithms for walkthrough and related applications have grown into a significant area, spurred by the growth in the complexity of models and the need for highly interactive ways of navigating them. In this survey, we review the fundamental issues in visibility and conduct an overview of the visibility culling techniques developed in the last decade. The taxonomy we use distinguishes between pointbased and fromregion methods. Pointbased methods are further subdivided into object and imageprecision techniques, while fromregion approaches can take advantage of the cellandportal structure of architectural environments or handle generic scenes.
Searching for Mobile Intruders in a Polygonal Region by a Group of Mobile Searchers
 SIAM JOURNAL ON COMPUTING
"... The problem of searching for mobile intruders in a polygonal region by mobile searchers is considered. A searcher can move continuously inside a polygon holding a flashlight that emits a single ray of light whose direction can be changed continuously. The visibility of a searcher at any time instant ..."
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Cited by 123 (2 self)
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The problem of searching for mobile intruders in a polygonal region by mobile searchers is considered. A searcher can move continuously inside a polygon holding a flashlight that emits a single ray of light whose direction can be changed continuously. The visibility of a searcher at any time instant is limited to the points on the ray. The intruders can move continuously with unbounded speed. We denote by ps(P ) the polygon search number of a simple polygon P , which is the number of searchers necessary and sufficient to search P . Let n, r, b and g be the number of edges, the number of reflex vertices, the bushiness, and the size of a minimum guard set of P , respectively. In this paper, we present matching upper and (worst case) lower bounds of 1 + blog 3 (2b + 1)c on ps(P ). Also upper bounds on ps(P ) in terms of n; r and g are presented; ps(P ) 1 + blog 3 (n \Gamma 3)c; ps(P ) 1 + blog 3 rc, and ps(P ) 2 + dlog 2 ge. These upper bounds are tight or almost tight in the worst case, since we show that for any natural number s 2, there is a polygon P such that ps(P ) = log 3 (n + 1) = log 3 (2r + 3) = 1 + log 3 (2g \Gamma 1) = s.
VisibilityBased PursuitEvasion in a Polygonal Environment
 International Journal of Computational Geometry and Applications
, 1997
"... This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita. Our stud ..."
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Cited by 86 (26 self)
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This paper addresses the problem of planning the motion of one or more pursuers in a polygonal environment to eventually "see" an evader that is unpredictable, has unknown initial position, and is capable of moving arbitrarily fast. This problem was first introduced by Suzuki and Yamashita. Our study of this problem is motivated in part by robotics applications, such as surveillance with a mobile robot equipped with a camera that must find a moving target in a cluttered workspace. A few bounds are introduced, and a complete algorithm is presented for computing a successful motion strategy for a single pursuer. For simplyconnected free spaces, it is shown that the minimum number of pursuers required is \Theta(lg n). For multiplyconnected free spaces, the bound is \Theta( p h + lg n) pursuers for a polygon that has n edges and h holes. A set of problems that are solvable by a single pursuer and require a linear number of recontaminations is shown. The complete algorithm searches a f...
Art gallery and illumination problems
 In Handbook on Computational Geometry, Elsevier Science Publishers, J.R. Sack and
, 2000
"... How many guards are necessary, and how many are sufficient to patrol the paintings and works of art in an art gallery with n walls? This wonderfully naïve question of combinatorial geometry has, since its formulation, stimulated an increasing number of of papers and surveys. In 1987, J. O’Rourke pub ..."
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Cited by 86 (3 self)
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How many guards are necessary, and how many are sufficient to patrol the paintings and works of art in an art gallery with n walls? This wonderfully naïve question of combinatorial geometry has, since its formulation, stimulated an increasing number of of papers and surveys. In 1987, J. O’Rourke published his book Art Gallery Theorems and Algorithms which has further fueled this area of research. The present book is being written almost 10 years since the publication of O’Rourke’s book, and the need for an uptodate manuscript on Art Gallery or Illumination Problems is evident. Some important open problems stated in O’Rourke’s book, such as... have been solved. New directions of research have since been investigated, including: watchman routes, floodlight illumination problems, guards with limited visibility or mobility, illumination of families of convex sets on the plane, guarding of rectilinear polygons, and others. In this book, we study these results and try to give a complete
An autonomous mobile robot with a 3D laser range finder for 3D exploration and digitalization of indoor environments
, 2003
"... Digital 3D models of the environment are needed in rescue and inspection robotics, facility managements and architecture. This paper presents an automatic system for gaging and digitalization of 3D indoor environments. It consists of an autonomous mobile robot, a reliable 3D laser range finder and t ..."
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Cited by 86 (22 self)
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Digital 3D models of the environment are needed in rescue and inspection robotics, facility managements and architecture. This paper presents an automatic system for gaging and digitalization of 3D indoor environments. It consists of an autonomous mobile robot, a reliable 3D laser range finder and three elaborated software modules. The first module, a fast variant of the Iterative Closest Points algorithm, registers the 3D scans in a common coordinate system and relocalizes the robot. The second module, a next best view planner, computes the next nominal pose based on the acquired 3D data while avoiding complicated obstacles. The third module, a closedloop and globally stable motor controller, navigates the mobile robot to a nominal pose on the base of odometry and avoids collisions with dynamical obstacles. The 3D laser range finder acquires a 3D scan at this pose. The proposed method allows one to digitalize large indoor environments fast and reliably without any intervention and solves the SLAM problem. The results of two 3D digitalization experiments are presented using a fast octreebased visualization method.