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A probabilistic analysis of some tree algorithms
 ANNALS OF APPLIED PROBABILITY
, 2005
"... In this paper a general class of tree algorithms is analyzed. It is shown that, by using an appropriate probabilistic representation of the quantities of interest, the asymptotic behavior of these algorithms can be obtained quite easily without resorting to the usual complex analysis techniques. Thi ..."
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Cited by 16 (5 self)
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In this paper a general class of tree algorithms is analyzed. It is shown that, by using an appropriate probabilistic representation of the quantities of interest, the asymptotic behavior of these algorithms can be obtained quite easily without resorting to the usual complex analysis techniques. This approach gives a unified probabilistic treatment of these questions. It simplifies and extends some of the results known in this domain.
On the AllPairs ShortestPath Algorithm Of Moffat and Takaoka
, 1997
"... We review how to solve the allpairs shortestpath problem in a nonnegatively Ž 2 weighted digraph with n vertices in expected time On log n.. This bound is shown to hold with high probability for a wide class of probability distributions on nonnegatively weighted digraphs. We also prove that, for ..."
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Cited by 11 (4 self)
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We review how to solve the allpairs shortestpath problem in a nonnegatively Ž 2 weighted digraph with n vertices in expected time On log n.. This bound is shown to hold with high probability for a wide class of probability distributions on nonnegatively weighted digraphs. We also prove that, for a large class of probability distributions, �Ž n log n. time is necessary with high probability to compute shortestpath distances with respect to a single
Probabilistic transforms for combinatorial urn models
 Combin. Probab. Comput
, 2002
"... In this paper, we present several probabilistic transforms related to classical urn models. These transforms render the dependent random variables describing the urn occupancies into independent random variables with appropriate distributions. This simplifies the analysis of a large number of proble ..."
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Cited by 8 (1 self)
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In this paper, we present several probabilistic transforms related to classical urn models. These transforms render the dependent random variables describing the urn occupancies into independent random variables with appropriate distributions. This simplifies the analysis of a large number of problems for which a function under investigation depends on the urn occupancies. The approach used for constructing the transforms involves generating functions of combinatorial numbers. We also show, by using Tauberian theorems derived in this paper, that under certain conditions the asymptotic expressions of target functions in the transform domain are identical to the asymptotic expressions in the inverse–transform domain. Therefore, asymptotic information about certain statistics can be gained without evaluating the inverse transform. 1
Effective supraclassifiers for knowledge base construction
, 1999
"... We explore the use of the supraclassifier framework in the construction of a classifier knowledge base. Previously, we introduced this framework within which labels produced by old classifiers are used to improve the generalization performance of a new classifier for a different but related classif ..."
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Cited by 8 (6 self)
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We explore the use of the supraclassifier framework in the construction of a classifier knowledge base. Previously, we introduced this framework within which labels produced by old classifiers are used to improve the generalization performance of a new classifier for a different but related classification task (Bollacker and Ghosh, 1998). We showed empirically that a simple Hamming nearest neighbor is superior to other techniques (e.g., multilayer perception (MLP), decision trees, Naive Bayes, Combiners) as a supraclassifier. Here, we describe theoretically how the probability that the Hamming nearest neighbor supraclassifier will predict the true target class approaches certainty at an exponential rate as more classifiers are reused. The scalability of the Hamming nearest neighbor with large numbers of previously created classifiers makes it a good choice as a supraclassifier in the application of building a repository of domain knowledge organized as a classifier knowledge base.
Generating Random Benchmarks for Description Logics
 In Proceedings of DL'98
, 1998
"... this paper, we address the problem of generating ..."
An efficient algorithm for the approximate median selection problem
 in Proceedings of the 4th Italian Conference on Algorithms and Complexity, ser. Lecture Notes in Computer Sciences
, 2000
"... We present an efficient algorithm for the approximate median selection problem. The algorithm works inplace; it is fast and easy to implement. For a large array it returns, with high probability, a very good estimate of the true median. The running time is linear in the length n of the input. The a ..."
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Cited by 7 (1 self)
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We present an efficient algorithm for the approximate median selection problem. The algorithm works inplace; it is fast and easy to implement. For a large array it returns, with high probability, a very good estimate of the true median. The running time is linear in the length n of the input. The algorithm performs fewer than 4 1 3n comparisons and 3n exchanges on the average. We present analytical results of the performance of the algorithm, as well as experimental illustrations of its precision. 1.
Precise Definition Of Software Component Specifications
 Proceedings of the IFAC ComputerAided Control System Design Conference
, 1997
"... : A set of generic specification categories is presented which can be used to comprehensively define any software component within a certain class. With these categories as a template, a specific set of formal specifications can be generated for each component. Specifications for a particular compon ..."
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Cited by 7 (6 self)
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: A set of generic specification categories is presented which can be used to comprehensively define any software component within a certain class. With these categories as a template, a specific set of formal specifications can be generated for each component. Specifications for a particular component (an algorithm that estimates the position and orientation of a physical object using visual sensing) have been defined in EXPRESS, an information modeling language. A few example natural language specifications are presented for this particular component. Keywords: Components, Computer vision, Formal languages, Formal specification, Software engineering, Software metrics, Software performance, Software specification, Software tools 1. INTRODUCTION The following is the software system development sequence that this research addresses: . A new software component is created, and the component developer (i.e., the vendor) wants see it widely used . A software systems developer (i.e., the use...
Optimal average case sorting on arrays
 Proceedings of the 12th Symposium on Theoretical Aspects of Computer Science, number 900 in Lecture Notes in Computer Science
, 1995
"... Abstract. We present algorithms for sorting and routing on twodimensional meshconnected parallel architectures that are optimal on average. If one processor has many packets then we asymptotically halve the up to now best running times. For a load of one optimal algorithms are known for the mesh. ..."
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Cited by 7 (2 self)
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Abstract. We present algorithms for sorting and routing on twodimensional meshconnected parallel architectures that are optimal on average. If one processor has many packets then we asymptotically halve the up to now best running times. For a load of one optimal algorithms are known for the mesh. We improve this to a load of eight without increasing the running time. For tori no optimal algorithms were known even for a load of one. Our algorithm is optimal for every load. Other architectures we consider include meshes with diagonals and reconfigurable meshes. Furthermore, the method applies to meshes of arbitrary higher dimensions and also enables optimal solutions for the routing problem. 1 Introduction We present deterministic algorithms that sort and route on meshconnected computers fast on average. For important, fundamental classes of problems (so called hh relations) we completely solve the problem in that sense that our approach is optimal for all cases. (We present matching lower bounds.) A twodimensional meshconnected computer is a processor array, where each processor has one bidirectional connection to each of its four neighbors. Meshes are a promising parallel architecture due to their scalability, their regular interconnection structure with its locality of communication, and since they need only linear space in the VLSImodel. We also consider meshes with wraparound connections, also known as tori, meshes with additional diagonal connections, and reconfigurable meshes.
Linear Waste of Best Fit Bin Packing on Skewed Distributions
 in Proceedings of the 41st Annual Symposium on Foundations of Computer Science, IEEE Computer Society Press, Los Alamitos, CA
, 2000
"... We prove that Best Fit bin packing has linear waste on the discrete distribution U{j, k} (where items are drawn uniformly from the set 2/k, , j/k}) for sufficiently large k when j = #k and 0.66 # < 2/3. Our results extend to continuous skewed distributions, where items are drawn unif ..."
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Cited by 6 (1 self)
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We prove that Best Fit bin packing has linear waste on the discrete distribution U{j, k} (where items are drawn uniformly from the set 2/k, , j/k}) for sufficiently large k when j = #k and 0.66 # < 2/3. Our results extend to continuous skewed distributions, where items are drawn uniformly on [0, a], for 0.66 a < 2/3. This implies that the expected asymptotic performance ratio of Best Fit is strictly greater than 1 for these distributions.
Toward a usable theory of Chernoff Bounds for heterogeneous and partially dependent random variables
, 1992
"... Let X be a sum of real valued random variables and have a bounded mean E[X]. The generic ChernoffHoeffding estimate for large deviations of X is: P rfX \GammaE[X ] ag min 0 e \Gamma(a+E[X]) E[e X ], which applies with a 0 to random variables with very small tails. At issue is how to use this ..."
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Cited by 6 (1 self)
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Let X be a sum of real valued random variables and have a bounded mean E[X]. The generic ChernoffHoeffding estimate for large deviations of X is: P rfX \GammaE[X ] ag min 0 e \Gamma(a+E[X]) E[e X ], which applies with a 0 to random variables with very small tails. At issue is how to use this method to attain sharp and useful estimates. We present a number of ChernoffHoeffding bounds for sums of random variables that may have a variety of dependent relationships and that may be heterogeneously distributed. AMS classifications 60F10, Large deviations, 68Q25 Analysis of algorithms, 62E17, Approximations to distributions (nonasymptotic), 60E15, Inequalities. Key words: Hoeffding bounds, Chernoff bounds, dependent random variables, Bernoulli trials. This research was supported, in part, by grants NSFCCR8902221, NSFCCR8906949, and NSFCCR9204202. 1 Summary In the analysis of probabilistic algorithms, some of the following problems may arise, possibly in complex combinations....