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A Decomposition of MultiDimensional Point Sets with Applications to kNearestNeighbors and nBody Potential Fields
 J. ACM
, 1992
"... We define the notion of a wellseparated pair decomposition of points in ddimensional space. We then develop efficient sequential and parallel algorithms for computing such a decomposition. We apply the resulting decomposition to the efficient computation of knearest neighbors and nbody potential ..."
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Cited by 240 (4 self)
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We define the notion of a wellseparated pair decomposition of points in ddimensional space. We then develop efficient sequential and parallel algorithms for computing such a decomposition. We apply the resulting decomposition to the efficient computation of knearest neighbors and nbody potential fields.
Parallel Algorithms with Optimal Speedup for Bounded Treewidth
 Proceedings 22nd International Colloquium on Automata, Languages and Programming
, 1995
"... We describe the first parallel algorithm with optimal speedup for constructing minimumwidth tree decompositions of graphs of bounded treewidth. On nvertex input graphs, the algorithm works in O((logn)^2) time using O(n) operations on the EREW PRAM. We also give faster parallel algorithms with opti ..."
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Cited by 32 (10 self)
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We describe the first parallel algorithm with optimal speedup for constructing minimumwidth tree decompositions of graphs of bounded treewidth. On nvertex input graphs, the algorithm works in O((logn)^2) time using O(n) operations on the EREW PRAM. We also give faster parallel algorithms with optimal speedup for the problem of deciding whether the treewidth of an input graph is bounded by a given constant and for a variety of problems on graphs of bounded treewidth, including all decision problems expressible in monadic secondorder logic. On nvertex input graphs, the algorithms use O(n) operations together with O(log n log n) time on the EREW PRAM, or O(log n) time on the CRCW PRAM.
Parallel Tree Contraction Part 2: Further Applications
 SIAM JOURNAL ON COMPUTING
, 1991
"... This paper applies the parallel tree contraction techniques developed in Miller and paper [Randomness and Computation, 5, S. Micali, ed., JAI Press, 1989, pp. 4772] to a number of fundamental graph problems. The paper presents an time and processor, a 0sided randomized algorithm for testing the i ..."
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Cited by 30 (3 self)
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This paper applies the parallel tree contraction techniques developed in Miller and paper [Randomness and Computation, 5, S. Micali, ed., JAI Press, 1989, pp. 4772] to a number of fundamental graph problems. The paper presents an time and processor, a 0sided randomized algorithm for testing the isomorphism of trees, and an n) time, nprocessor algorithm for maximal isomorphism and for common subexpression elimination. An time, nprocessor algorithm for computing the canonical forms of trees and subtrees is given. An Ologn time algorithm for computing the tree of 3connected components of a graph, an n)time algorithm for computing an explicit planar embedding of a planar graph, and an n)time algorithm for computing a canonical form for a planar graph are also given. All these latter algorithms use only processors on a Parallel Random Access Machine (PRAM) model with concurrent writes and concurrent reads.
Visibility with a moving point of view
 Algorithmica
, 1994
"... We investigate 3d visibility problems in which the viewing position moves along a straight flightpath. Specifically we focus on two problems: determining the points along the flightpath at which the topology of the viewed scene changes, and answering rayshooting queries for rays with origin on the ..."
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Cited by 28 (1 self)
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We investigate 3d visibility problems in which the viewing position moves along a straight flightpath. Specifically we focus on two problems: determining the points along the flightpath at which the topology of the viewed scene changes, and answering rayshooting queries for rays with origin on the flightpath. Three progressively more specialized problems are considered: general scenes, terrains, and terrains with vertical flightpaths. 1.
Optimal Parallel AllNearestNeighbors Using the WellSeparated Pair Decomposition
 In Proc. 34th IEEE Symposium on Foundations of Computer Science
, 1993
"... We present an optimal parallel algorithm to construct the wellseparated pair decomposition of a point set P in ! d . We show how this leads to a deterministic optimal O(logn) time parallel algorithm for finding the knearestneighbors of each point in P , where k is a constant. We discuss severa ..."
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Cited by 27 (1 self)
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We present an optimal parallel algorithm to construct the wellseparated pair decomposition of a point set P in ! d . We show how this leads to a deterministic optimal O(logn) time parallel algorithm for finding the knearestneighbors of each point in P , where k is a constant. We discuss several additional applications of the wellseparated pair decomposition for which we can derive faster parallel algorithms. 1 Introduction In [4] we introduced the wellseparated pair decomposition of a set P of n points in ! d , and showed how to apply this decomposition to develop efficient parallel algorithms for two problems posed on multidimensional point sets. One of these applications led to the fastest known deterministic parallel algorithm for finding the knearestneighbors of each point in P using O(n) processors. The time required for this algorithm is \Theta(log 2 n), which is within a log n factor of optimal. In this paper, we close the gap by developing an optimal O(log n) ti...
Parallel Open Ear Decomposition with Applications to Graph Biconnectivity and Triconnectivity
 Synthesis of Parallel Algorithms
, 1992
"... This report deals with a parallel algorithmic technique that has proved to be very useful in the design of efficient parallel algorithms for several problems on undirected graphs. We describe this method for searching undirected graphs, called "open ear decomposition", and we relate this decompos ..."
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Cited by 25 (9 self)
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This report deals with a parallel algorithmic technique that has proved to be very useful in the design of efficient parallel algorithms for several problems on undirected graphs. We describe this method for searching undirected graphs, called "open ear decomposition", and we relate this decomposition to graph biconnectivity. We present an efficient parallel algorithm for finding this decomposition and we relate it to a sequential algorithm based on depthfirst search. We then apply open ear decomposition to obtain an efficient parallel algorithm for testing graph triconnectivity and for finding the triconnnected components of a graph.
Evaluating Arithmetic Expressions Using Tree Contraction: A Fast and Scalable Parallel Implementation for Symmetric Multiprocessors (SMPs)
 Proc. 9th Intâ€™l Conf. on High Performance Computing (HiPC 2002), volume 2552 of Lecture Notes in Computer Science
, 2002
"... The ability to provide uniform sharedmemory access to a significant number of processors in a single SMP node brings us much closer to the ideal PRAM parallel computer. In this paper, we develop new techniques for designing a uniform sharedmemory algorithm from a PRAM algorithm and present the res ..."
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Cited by 23 (7 self)
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The ability to provide uniform sharedmemory access to a significant number of processors in a single SMP node brings us much closer to the ideal PRAM parallel computer. In this paper, we develop new techniques for designing a uniform sharedmemory algorithm from a PRAM algorithm and present the results of an extensive experimental study demonstrating that the resulting programs scale nearly linearly across a significant range of processors and across the entire range of instance sizes tested. This linear speedup with the number of processors is one of the first ever attained in practice for intricate combinatorial problems. The example we present in detail here is for evaluating arithmetic expression trees using the algorithmic techniques of list ranking and tree contraction; this problem is not only of interest in its own right, but is representativeof a large class of irregular combinatorial problems that have simple and efficient sequential implementations and fast PRAM algorithms, but have no known efficient parallel implementations. Our results thus offer promise for bridging the gap between the theory and practice of sharedmemory parallel algorithms.
LogarithmicTime Updates and Queries in Probabilistic Networks
 Journal of Artificial Intelligence Research
, 1995
"... Traditional databases commonly support efficient query and update procedures that operate in time which is sublinear in the size of the database. Our goal in this paper is to take a first step toward dynamic reasoning in probabilistic databases with comparable efficiency. We propose a dynamic data s ..."
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Cited by 18 (0 self)
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Traditional databases commonly support efficient query and update procedures that operate in time which is sublinear in the size of the database. Our goal in this paper is to take a first step toward dynamic reasoning in probabilistic databases with comparable efficiency. We propose a dynamic data structure that supports efficient algorithms for updating and querying singly connected Bayesian networks. In the conventional algorithm, new evidence is absorbed in time O(1) and queries are processed in time O(N ), where N is the size of the network. We propose an algorithm which, after a preprocessing phase, allows us to answer queries in time O(logN ) at the expense of O(logN ) time per evidence absorption. The usefulness of sublinear processing time manifests itself in applications requiring (near) realtime response over large probabilistic databases. We briefly discuss a potential application of dynamic probabilistic reasoning in computational biology. 1. Introduction Probabilistic ...
The Owner Concept for PRAMs
, 1991
"... We analyze the owner concept for PRAMs. In OROWPRAMs each memory cell has one distinct processor that is the only one allowed to write into this memory cell and one distinct processor that is the only one allowed to read from it. By symmetric pointer doubling, a new proof technique for OROWPRAMs, ..."
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Cited by 17 (5 self)
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We analyze the owner concept for PRAMs. In OROWPRAMs each memory cell has one distinct processor that is the only one allowed to write into this memory cell and one distinct processor that is the only one allowed to read from it. By symmetric pointer doubling, a new proof technique for OROWPRAMs, it is shown that list ranking can be done in O(log n) time by an OROWPRAM and that LOGSPACE ` OROWTIME(log n). Then we prove that OROWPRAMs are a fairly robust model and recognize the same class of languages when the model is modified in several ways and that all kinds of PRAMs intertwine with the NC hierarchy without timeloss. Finally it is shown that EREWPRAMs can be simulated by OREWPRAMs and ERCWPRAMs by ORCWPRAMs. 3 This research was partially supported by the Deutsche Forschungsgemeinschaft, SFB 342, Teilprojekt A4 "Klassifikation und Parallelisierung durch Reduktionsanalyse" y Email: rossmani@lan.informatik.tumuenchen.dbp.de Introduction Fortune and Wyllie introduced in...
Optimal Routing of Parentheses on the Hypercube
 IN PROCEEDINGS OF THE SYMPOSIUM ON PARALLEL ARCHITECTURES AND ALGORITHMS
, 1994
"... We consider a new class of routing requests or partial permutations for which we give optimal online routing algorithms on the hypercube and shuffleexchange network. For wellformed words of parentheses our algorithm establishes communication between all matching pairs in logarithmic time. It can ..."
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Cited by 14 (6 self)
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We consider a new class of routing requests or partial permutations for which we give optimal online routing algorithms on the hypercube and shuffleexchange network. For wellformed words of parentheses our algorithm establishes communication between all matching pairs in logarithmic time. It can be applied to the membership problem for Dyck languages and a number of problems for algebraic expressions.