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Voronoi diagrams  a survey of a fundamental geometric data structure
 ACM COMPUTING SURVEYS
, 1991
"... This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. ..."
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Cited by 560 (5 self)
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This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. The paper puts particular emphasis on the unified exposition of its mathematical and algorithmic properties. Finally, the paper provides the first comprehensive bibliography on Voronoi diagrams and related structures.
Bullet: High Bandwidth Data Dissemination Using an Overlay Mesh
, 2003
"... In recent years, overlay networks have become an effective alternative to IP multicast for efficient point to multipoint communication across the Internet. Typically, nodes selforganize with the goal of forming an efficient overlay tree, one that meets performance targets without placing undue burd ..."
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Cited by 354 (21 self)
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In recent years, overlay networks have become an effective alternative to IP multicast for efficient point to multipoint communication across the Internet. Typically, nodes selforganize with the goal of forming an efficient overlay tree, one that meets performance targets without placing undue burden on the underlying network. In this paper, we target highbandwidth data distribution from a single source to a large number of receivers. Applications include largefile transfers and realtime multimedia streaming. For these applications, we argue that an overlay mesh, rather than a tree, can deliver fundamentally higher bandwidth and reliability relative to typical tree structures. This paper presents Bullet, a scalable and distributed algorithm that enables nodes spread across the Internet to selforganize into a high bandwidth overlay mesh. We construct Bullet around the insight that data should be distributed in a disjoint manner to strategic points in the network. Individual Bullet receivers are then responsible for locating and retrieving the data from multiple points in parallel. Key contributions of this work include: i) an algorithm that sends data to di#erent points in the overlay such that any data object is equally likely to appear at any node, ii) a scalable and decentralized algorithm that allows nodes to locate and recover missing data items, and iii) a complete implementation and evaluation of Bullet running across the Internet and in a largescale emulation environment reveals up to a factor two bandwidth improvements under a variety of circumstances. In addition, we find that, relative to treebased solutions, Bullet reduces the need to perform expensive bandwidth probing.
Design and Analysis of an MSTBased Topology Control Algorithm
, 2002
"... In this paper, we present a Minimum Spanning Tree (MST) based topology control algorithm, called Local Minimum Spanning Tree (LMST), for wireless multihop networks. In this algorithm, each node builds its local minimum spanning tree independently and only keeps ontree nodes that are onehop away a ..."
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Cited by 189 (4 self)
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In this paper, we present a Minimum Spanning Tree (MST) based topology control algorithm, called Local Minimum Spanning Tree (LMST), for wireless multihop networks. In this algorithm, each node builds its local minimum spanning tree independently and only keeps ontree nodes that are onehop away as its neighbors in the final topology. We analytically prove several important properties of LMST: (1) the topology derived under LMST preserves the network connectivity; (2) the node degree of any node in the resulting topology is bounded by 6; and (3) the topology can be transformed into one with bidirectional links (without impairing the network connectivity) after removal of all unidirectional links. These results are corroborated in the simulation study.
An Overview of QualityofService Routing for the Next Generation HighSpeed Networks: Problems and Solutions
"... The upcoming Gbps highspeed networks are expected to support a wide range of communicationintensive, realtime multimedia applications. The requirement for timely delivery of digitized audiovisual information raises new challenges for the next generation integratedservice broadband networks. On ..."
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Cited by 182 (17 self)
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The upcoming Gbps highspeed networks are expected to support a wide range of communicationintensive, realtime multimedia applications. The requirement for timely delivery of digitized audiovisual information raises new challenges for the next generation integratedservice broadband networks. One of the key issues is the QualityofService (QoS) routing. It selects network routes with sufficient resources for the requested QoS parameters. The goal of routing solutions is twofold: (1) satisfying the QoS requirements for every admitted connection and (2) achieving the global efficiency in resource utilization. Many unicast/multicast QoS routing algorithms were published recently, and they work with a variety of QoS requirements and resource constraints. Overall, they can be partitioned into three broad classes: (1) source routing, (2) distributed routing and (3) hierarchical routing algorithms. In this paper we give an overview of the QoS routing problem as well as the existing solutions. We present the strengths and the weaknesses of different routing strategies and outline the challenges. We also discuss the basic algorithms in each class, classify and compare them, and point out possible future directions in the QoS routing area.
An effective implementation of the linkernighan traveling salesman heuristic
 European Journal of Operational Research
, 2000
"... This report describes an implementation of the LinKernighan heuristic, one of the most successful methods for generating optimal or nearoptimal solutions for the symmetric traveling salesman problem. Computational tests show that the implementation is highly effective. It has found optimal solution ..."
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Cited by 120 (1 self)
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This report describes an implementation of the LinKernighan heuristic, one of the most successful methods for generating optimal or nearoptimal solutions for the symmetric traveling salesman problem. Computational tests show that the implementation is highly effective. It has found optimal solutions for all solved problem instances we have been able to obtain, including a 7397city problem (the largest nontrivial problem instance solved to optimality today). Furthermore, the algorithm has improved the best known solutions for a series of largescale problems with unknown optima, among these an 85900city problem. 1.
Using Optimal DependencyTrees for Combinatorial Optimization: Learning the Structure of the Search Space
, 1997
"... Many combinatorial optimization algorithms have no mechanism to capture interparameter dependencies. However, modeling such dependencies may allow an algorithm to concentrate its sampling more effectively on regions of the search space which have appeared promising in the past. We present an algori ..."
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Cited by 114 (2 self)
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Many combinatorial optimization algorithms have no mechanism to capture interparameter dependencies. However, modeling such dependencies may allow an algorithm to concentrate its sampling more effectively on regions of the search space which have appeared promising in the past. We present an algorithm which incrementally learns secondorder probability distributions from good solutions seen so far, uses these statistics to generate optimal (in terms of maximum likelihood) dependency trees to model these distributions, and then stochastically generates new candidate solutions from these trees. We test this algorithm on a variety of optimization problems. Our results indicate superior performance over other tested algorithms that either (1) do not explicitly use these dependencies, or (2) use these dependencies to generate a more restricted class of dependency graphs. Scott Davies was supported by a Graduate Student Research Fellowship from the National Science Foundation. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied of the National Science Foundation. Keywords:
Automatic Data Partitioning on Distributed Memory Multiprocessors
, 1991
"... An important problem facing numerous research projects on parallelizing compilers for distributed memory machines is that of automatically determining a suitable data partitioning scheme for a program. Most of the current projects leave this tedious problem almost entirely to the user. In this paper ..."
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Cited by 102 (6 self)
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An important problem facing numerous research projects on parallelizing compilers for distributed memory machines is that of automatically determining a suitable data partitioning scheme for a program. Most of the current projects leave this tedious problem almost entirely to the user. In this paper, we present a novel approach to the problem of automatic data partitioning. We introduce the notion of constraints on data distribution, and show how, based on performance considerations, a compiler identifies constraints to be imposed on the distribution of various data structures. These constraints are then combined by the compiler to obtain a complete and consistent picture of the data distribution scheme, one that offers good performance in terms of the overall execution time.
Parallel Algorithms for Hierarchical Clustering
 Parallel Computing
, 1995
"... Hierarchical clustering is a common method used to determine clusters of similar data points in multidimensional spaces. O(n 2 ) algorithms are known for this problem [3, 4, 10, 18]. This paper reviews important results for sequential algorithms and describes previous work on parallel algorithms f ..."
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Cited by 80 (1 self)
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Hierarchical clustering is a common method used to determine clusters of similar data points in multidimensional spaces. O(n 2 ) algorithms are known for this problem [3, 4, 10, 18]. This paper reviews important results for sequential algorithms and describes previous work on parallel algorithms for hierarchical clustering. Parallel algorithms to perform hierarchical clustering using several distance metrics are then described. Optimal PRAM algorithms using n log n processors are given for the average link, complete link, centroid, median, and minimum variance metrics. Optimal butterfly and tree algorithms using n log n processors are given for the centroid, median, and minimum variance metrics. Optimal asymptotic speedups are achieved for the best practical algorithm to perform clustering using the single link metric on a n log n processor PRAM, butterfly, or tree. Keywords. Hierarchical clustering, pattern analysis, parallel algorithm, butterfly network, PRAM algorithm. 1 In...
Evaluation of multicast routing algorithms for realtime communication on highspeed networks
 IEEE Journal on Selected Areas in Communications
, 1997
"... Multicast (MC) routing algorithms capable of satisfying the quality of service (QoS) requirements of realtime applications will be essential for future highspeed networks. We compare the performance of all of the important MC routing algorithms when applied to networks with asymmetric link loads. ..."
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Cited by 78 (4 self)
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Multicast (MC) routing algorithms capable of satisfying the quality of service (QoS) requirements of realtime applications will be essential for future highspeed networks. We compare the performance of all of the important MC routing algorithms when applied to networks with asymmetric link loads. Each algorithm is judged based on the quality of the MC trees it generates and its efficiency in managing the network resources. Simulation results over random networks show that unconstrained algorithms are not capable of fulfilling the QoS requirements of realtime applications in widearea networks. Simulations also reveal that one of the unconstrained algorithms, reverse path multicasting (RPM), is quite inefficient when applied to asymmetric networks. We study how combining routing with resource reservation and admission control improves RPM’s efficiency in managing the network resources. The performance of one semiconstrained heuristic, MSC, three constrained Steiner tree (CST) heuristics, KPP, CAO, and BSMA, and one constrained shortest path tree (CSPT) heuristic, CDKS are also studied. Simulations show that the semiconstrained and constrained heuristics are capable of successfully constructing MC trees which satisfy the QoS requirements of realtime traffic. However, the cost performance of the heuristics varies. BSMA’s MC trees are lower in cost than all other constrained heuristics. Finally, we compare the execution times of all algorithms, unconstrained, semiconstrained, and constrained.