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Geometric Range Searching
, 1994
"... In geometric range searching, algorithmic problems of the following type are considered: Given an npoint set P in the plane, build a data structure so that, given a query triangle R, the number of points of P lying in R can be determined quickly. Problems of this type are of crucial importance in c ..."
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Cited by 46 (2 self)
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In geometric range searching, algorithmic problems of the following type are considered: Given an npoint set P in the plane, build a data structure so that, given a query triangle R, the number of points of P lying in R can be determined quickly. Problems of this type are of crucial importance in computational geometry, as they can be used as subroutines in many seemingly unrelated algorithms. We present a survey of results and main techniques in this area.
Randomization and Derandomization in SpaceBounded Computation
 In Proceedings of the 11th Annual IEEE Conference on Computational Complexity
, 1996
"... This is a survey of spacebounded probabilistic computation, summarizing the present state of knowledge about the relationships between the various complexity classes associated with such computation. The survey especially emphasizes recent progress in the construction of pseudorandom generators tha ..."
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Cited by 36 (0 self)
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This is a survey of spacebounded probabilistic computation, summarizing the present state of knowledge about the relationships between the various complexity classes associated with such computation. The survey especially emphasizes recent progress in the construction of pseudorandom generators that fool probabilistic spacebounded computations, and the application of such generators to obtain deterministic simulations.
Clustering Motion
 In Proc. 42nd Annu. IEEE Sympos. Found. Comput. Sci
, 2003
"... Given a set of moving points in IR , we show how to cluster them in advance, using a small number of clusters, so that at any time this static clustering is competitive with the optimal kcenter clustering at that time. The advantage of this approach is that it avoids updating the clustering a ..."
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Cited by 29 (5 self)
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Given a set of moving points in IR , we show how to cluster them in advance, using a small number of clusters, so that at any time this static clustering is competitive with the optimal kcenter clustering at that time. The advantage of this approach is that it avoids updating the clustering as time passes. We also show how to maintain this static clustering eciently under insertions and deletions.
Iterative Dynamic Load Balancing in Multicomputers
 Journal of Operational Research Society
, 1994
"... Dynamic load balancing in multicomputers can improve the utilization of processors and the efficiency of parallel computations through migrating workload across processors at runtime. We present a survey and critique of dynamic load balancing strategies that are iterative: workload migration is car ..."
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Cited by 21 (3 self)
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Dynamic load balancing in multicomputers can improve the utilization of processors and the efficiency of parallel computations through migrating workload across processors at runtime. We present a survey and critique of dynamic load balancing strategies that are iterative: workload migration is carried out through transferring processes across nearest neighbor processors. Iterative strategies have become prominent in recent years because of the increasing popularity of pointtopoint interconnection networks for multicomputers. Key words: dynamic load balancing, multicomputers, optimization, queueing theory, scheduling. INTRODUCTION Multicomputers are highly concurrent systems that are composed of many autonomous processors connected by a communication network 1;2 . To improve the utilization of the processors, parallel computations in multicomputers require that processes be distributed to processors in such a way that the computational load is evenly spread among the processors...
Ultrafast expected time parallel algorithms
 Proc. of the 2nd SODA
, 1991
"... It has been shown previously that sorting n items into n locations with a polynomial number of processors requires Ω(log n/log log n) time. We sidestep this lower bound with the idea of Padded Sorting, or sorting n items into n + o(n) locations. Since many problems do not rely on the exact rank of s ..."
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Cited by 20 (3 self)
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It has been shown previously that sorting n items into n locations with a polynomial number of processors requires Ω(log n/log log n) time. We sidestep this lower bound with the idea of Padded Sorting, or sorting n items into n + o(n) locations. Since many problems do not rely on the exact rank of sorted items, a Padded Sort is often just as useful as an unpadded sort. Our algorithm for Padded Sort runs on the Tolerant CRCW PRAM and takes Θ(log log n/log log log n) expected time using n log log log n/log log n processors, assuming the items are taken from a uniform distribution. Using similar techniques we solve some computational geometry problems, including Voronoi Diagram, with the same processor and time bounds, assuming points are taken from a uniform distribution in the unit square. Further, we present an Arbitrary CRCW PRAM algorithm to solve the Closest Pair problem in constant expected time with n processors regardless of the distribution of points. All of these algorithms achieve linear speedup in expected time over their optimal serial counterparts. 1 Research done while at the University of Michigan and supported by an AT&T Fellowship.
Computational Complexity, Protein Structure Prediction, and the Levinthal Paradox
 Computational Complexity Protein Structure Prediction and the Levinthal Paradox
, 1994
"... The task of determining the globally optimal (minimumenergy) conformation of a protein given its potentialenergy function is widely believed to require an amount of computer time that is exponential in the number of soft degrees of freedom in the protein. Conventional reasoning as to the exponenti ..."
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Cited by 19 (0 self)
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The task of determining the globally optimal (minimumenergy) conformation of a protein given its potentialenergy function is widely believed to require an amount of computer time that is exponential in the number of soft degrees of freedom in the protein. Conventional reasoning as to the exponential time complexity of this problem is fallaciousit is based solely on the size of the search spaceand for some variants of the proteinstructure prediction problem the conclusion is likely to be incorrect. Every problem in combinatorial optimization has an exponential number of candidate solutions, but many such problems can be solved by algorithms that do not require exponential time. We present a critical review of efforts to characterize rigorously the computational requirements of global potentialenergy minimization for a polypeptide chain that has a unique energy minimum corresponding to the native structure of the protein. An argument by Crippen (1975) demonstrated that an algor...
An overview of computational complexity
 Communications of the ACM
, 1983
"... foremost recognition of technical contributions to the computing community. The citation of Cook's achievements noted that "Dr. Cook has advanced our understanding of the complexity of computation in a significant and profound way. His seminal paper, The Complexity of Theorem Proving Procedures ..."
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Cited by 17 (0 self)
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foremost recognition of technical contributions to the computing community. The citation of Cook's achievements noted that "Dr. Cook has advanced our understanding of the complexity of computation in a significant and profound way. His seminal paper, The Complexity of Theorem Proving Procedures, presented at the 1971 ACM SIGACT Symposium on the Theory of Computing, laid the foundations for the theory of NPcompleteness. The ensuing exploration of the boundaries and nature of the NPcomplete class of problems has been one of the most active and important research activities in computer science for the last decade. Cook is well known for his influential results in fundamental areas of computer science. He has made significant contributions to complexity theory, to timespace tradeoffs in computation, and to logics for programming languages. His work is characterized by elegance and insights and has illuminated the very nature of computation." During 19701979, Cook did extensive work under grants from the
Fast Algorithms for Computing the Smallest kEnclosing Disc
 In Proc. 11th Annu. European Sympos. Algorithms, volume 2832 of Lect. Notes in Comp. Sci
, 2003
"... We consider the problem of nding, for a given n point set P in the plane and an integer k n, the smallest circle enclosing at least k points of P . We present a randomized algorithm that computes in O(nk) expected time such a circle, improving over previously known algorithms. ..."
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Cited by 16 (3 self)
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We consider the problem of nding, for a given n point set P in the plane and an integer k n, the smallest circle enclosing at least k points of P . We present a randomized algorithm that computes in O(nk) expected time such a circle, improving over previously known algorithms.
Abstractions for Constructing Dependable Distributed Systems
, 1992
"... ions for Constructing Dependable Distributed Systems Shivakant Mishra 1 and Richard D. Schlichting TR 9219 Abstract Distributed systems, in which multiple machines are connected by a communications network, are often used to build highly dependable computing systems. However, constructing the softw ..."
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Cited by 15 (3 self)
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ions for Constructing Dependable Distributed Systems Shivakant Mishra 1 and Richard D. Schlichting TR 9219 Abstract Distributed systems, in which multiple machines are connected by a communications network, are often used to build highly dependable computing systems. However, constructing the software required to realize such dependability is a difficult task since it requires the programmer to build faulttolerant software that can continue to function despite failures. To simplify this process, canonical structuring techniques or programming paradigms have been developed, including the object/action model, the primary/backup approach, the state machine approach, and conversations. In this paper, some of the system abstractions designed to support these paradigms are described. These abstractions, which are termed faulttolerant services, can be categorized into two types. One type provides functionality similar to standard hardware or operating system services, but with improved ...