Results 1  10
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187
Boundary Recognition in Sensor Networks by Topological Me ods
 in Proc. of MOBICOM
, 2006
"... Wireless sensor networks are tightly associated with the underlying environment in which the sensors are deployed. The global topology of the network is of great importance to both sensor network applications and the implementation of networking functionalities. In this paper we study the problem ..."
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Cited by 105 (17 self)
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Wireless sensor networks are tightly associated with the underlying environment in which the sensors are deployed. The global topology of the network is of great importance to both sensor network applications and the implementation of networking functionalities. In this paper we study the problem of topology discovery, in particular, identifying boundaries in a sensor network. Suppose a large number of sensor nodes are scattered in a geometric region, with nearby nodes communicating with each other directly. Our goal is to find the boundary nodes by using only connectivity information. We do not assume any knowledge of the node locations or interdistances, nor do we enforce that the communication graph follows the unit disk graph model. We propose a simple, distributed algorithm that correctly detects nodes on the boundaries and connects them into meaningful boundary cycles. We obtain as a byproduct the medial axis of the sensor field, which has applications in creating virtual coordinates for routing. We show by extensive simulation that the algorithm gives good results even for networks with low density. We also prove rigorously the correctness of the algorithm for continuous geometric domains.
Fast exact and approximate geodesics on meshes
 ACM Trans. Graph
, 2005
"... The computation of geodesic paths and distances on triangle meshes is a common operation in many computer graphics applications. We present several practical algorithms for computing such geodesics from a source point to one or all other points efficiently. First, we describe an implementation of th ..."
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Cited by 102 (0 self)
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The computation of geodesic paths and distances on triangle meshes is a common operation in many computer graphics applications. We present several practical algorithms for computing such geodesics from a source point to one or all other points efficiently. First, we describe an implementation of the exact “single source, all destination ” algorithm presented by Mitchell, Mount, and Papadimitriou (MMP). We show that the algorithm runs much faster in practice than suggested by worst case analysis. Next, we extend the algorithm with a merging operation to obtain computationally efficient and accurate approximations with bounded error. Finally, to compute the shortest path between two given points, we use a lowerbound property of our approximate geodesic algorithm to efficiently prune the frontier of the MMP algorithm, thereby obtaining an exact solution even more quickly.
Approximation algorithms for TSP with neighborhoods in the plane
 J. ALGORITHMS
, 2001
"... In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. As a generalization of the classical Euclidean TSP, TSPN is also NPhard. In this paper, we present new approximation results for the TSPN, incl ..."
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Cited by 89 (9 self)
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In the Euclidean TSP with neighborhoods (TSPN), we are given a collection of n regions (neighborhoods) and we seek a shortest tour that visits each region. As a generalization of the classical Euclidean TSP, TSPN is also NPhard. In this paper, we present new approximation results for the TSPN, including (1) a constantfactor approximation algorithm for the case of arbitrary connected neighborhoods having comparable diameters; and (2) a PTAS for the important special case of disjoint unit disk neighborhoods (or nearly disjoint, nearlyunit disks). Our methods also yield improved approximation ratios for various special classes of neighborhoods, which have previously been studied. Further, we give a lineartime O(1) approximation algorithm for the case of neighborhoods that are (innite) straight lines.
Modeling acoustics in virtual environments using the uniform theory of diffraction
 ACM Computer Graphics, SIGGRAPH’01 Proceedings
, 2001
"... Realistic modeling of reverberant sound in 3D virtual worlds provides users with important cues for localizing sound sources and understanding spatial properties of the environment. Unfortunately, current geometric acoustic modeling systems do not accurately simulate reverberant sound. Instead, they ..."
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Cited by 72 (10 self)
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Realistic modeling of reverberant sound in 3D virtual worlds provides users with important cues for localizing sound sources and understanding spatial properties of the environment. Unfortunately, current geometric acoustic modeling systems do not accurately simulate reverberant sound. Instead, they model only direct transmission and specular reflection, while diffraction is either ignored or modeled through statistical approximation. However, diffraction is important for correct interpretation of acoustic environments, especially when the direct path between sound source and receiver is occluded. The Uniform Theory of Diffraction (UTD) extends geometrical acoustics with diffraction phenomena: illuminated edges become secondary sources of diffracted rays that in turn may propagate through the environment. In this paper, we propose an efficient way for computing the acoustical effect of diffraction paths using the UTD for deriving secondary diffracted rays and associated diffraction coefficients. Our main contributions are: 1) a beam tracing method for enumerating sequences of diffracting edges efficiently and without aliasing in densely occluded polyhedral environments; 2) a practical approximation to the simulated sound field in which diffraction is considered only in shadow regions; and 3) a realtime auralization system demonstrating that diffraction dramatically improves the quality of spatialized sound in virtual environments.
Exact and Approximate Distances in Graphs  a survey
 In ESA
, 2001
"... We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different settings and models and try to identify some remaining open problems. ..."
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Cited by 68 (0 self)
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We survey recent and not so recent results related to the computation of exact and approximate distances, and corresponding shortest, or almost shortest, paths in graphs. We consider many different settings and models and try to identify some remaining open problems.
A constantfactor approximation algorithm for the k mst problem (extended abstract
 in Proceedings of the twentyeighth annual ACM symposium on Theory of computing (STOC ’96
, 1996
"... ABSTRACT In the Euclidean TSP with neighborhoods (TSPN) problem we seek a shortest tour that visits a given set of n neighborhoods. The Euclidean TSPN generalizes the standard TSP on points. We present the first constantfactor approximation algorithm for planar TSPN with pairwisedisjoint connecte ..."
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Cited by 58 (5 self)
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ABSTRACT In the Euclidean TSP with neighborhoods (TSPN) problem we seek a shortest tour that visits a given set of n neighborhoods. The Euclidean TSPN generalizes the standard TSP on points. We present the first constantfactor approximation algorithm for planar TSPN with pairwisedisjoint connected neighborhoods of any size or shape. Prior approximation bounds were O(log n), except in special cases. The methods also apply to the case of arbitrarily overlapping regions that are convex.
On the complexity of approximating TSP with neighborhoods and related problems
 Computational Complexity
"... We prove that various geometric covering problems, related to the Travelling Salesman Problem cannot be efficiently approximated to within any constant factor unless P = NP. This includes the GroupTravelling Salesman Problem (TSP with Neighborhoods) in the Euclidean plane, the GroupSteinerTree in ..."
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Cited by 36 (2 self)
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We prove that various geometric covering problems, related to the Travelling Salesman Problem cannot be efficiently approximated to within any constant factor unless P = NP. This includes the GroupTravelling Salesman Problem (TSP with Neighborhoods) in the Euclidean plane, the GroupSteinerTree in the Euclidean plane and the Minimum Watchman Tour and the Minimum Watchman Path in 3D. It resolves three open problems presented in the comprehensive survey of Mitchell [Mit00], improves a previously known approximation hardness factor of 2041 2040 [GL00, dBGK+ 02] for the first problem, and it is the first approximation hardness factor for the other problems. Some inapproximability factors are also shown for special cases of the above problems, where the size of the sets is bounded. GroupTSP and GroupSteinerTree where each neighbourhood is connected are also considered. It is shown that approximating these variants to within any constant factor smaller than 2, is NPhard. For the GroupTravelling Salesman and GroupSteinerTree Problems in dimension d, we show an innapproximability factor of O(log d−1 d HyperGraph VertexCover.
Approximate shortest path on a polyhedral surface and its applications
 ComputerAided Design
, 2000
"... A new algorithm is proposed for calculating the approximate shortest path on a polyhedral surface. The method mainly uses Dijkstra’s algorithm and is based on selective refinement of the discrete graph of a polyhedron. Although the algorithm is an approximation, it has the significant advantages of ..."
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Cited by 36 (1 self)
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A new algorithm is proposed for calculating the approximate shortest path on a polyhedral surface. The method mainly uses Dijkstra’s algorithm and is based on selective refinement of the discrete graph of a polyhedron. Although the algorithm is an approximation, it has the significant advantages of being fast, easy to implement, high approximation accuracy, and numerically robust. The approximation accuracy and computation time are compared between this approximation algorithm and the extended Chen & Han (ECH) algorithm that can calculate the exact shortest path for nonconvex polyhedra. The approximation algorithm can calculate shortest paths within 0.4 % accuracy to roughly 1001000 times faster than the ECH algorithm in our examples. Two applications are discussed of the approximation algorithm to geometric modeling.
Touring a sequence of polygons
 Proc. 35th ACM Sympos. Theory Comput
, 2003
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 36 (5 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Interactive decal compositing with discrete exponential maps
 ACM Trans. Graph
, 2006
"... Figure 1: A clay elephant statue (left) was modeled using sketchbased implicitsurface modeling software. Then, a lapped base texture and 25 feature textures were extracted from 22 images taken with a digital camera and composited on the surface. Photography, image creation, and texture positioning ..."
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Cited by 34 (7 self)
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Figure 1: A clay elephant statue (left) was modeled using sketchbased implicitsurface modeling software. Then, a lapped base texture and 25 feature textures were extracted from 22 images taken with a digital camera and composited on the surface. Photography, image creation, and texture positioning was completed in under an hour. A method is described for texturing surfaces using decals, images placed on the surface using local parameterizations. Decal parameterizations are generated with a novel O(N logN) discrete approximation to the exponential map which requires only a single additional step in Dijkstra’s graphdistance algorithm. Decals are dynamically composited in an interface that addresses many limitations of previous work. Tools for image processing, deformation/featurematching, and vector graphics are implemented using direct surface interaction. Exponential map decals can contain holes and can also be combined with conformal parameterization to reduce distortion. The exponential map approximation can be computed on any point set, including meshes and sampled implicit surfaces, and is relatively stable under resampling. The decals stick to the surface as it is interactively deformed, allowing the texture to be preserved even if the surface changes topology. These properties make exponential map decals a suitable approach for texturing animated implicit surfaces.