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133
Bounds On The Cover Time
 J. Theoretical Probab
, 1988
"... . Consider a particle that moves on a connected, undirected graph G with n vertices. At each step the particle goes from the current vertex to one of its neighbors, chosen uniformly at random. The cover time is the first time when the particle has visited all the vertices in the graph starting from ..."
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Cited by 48 (0 self)
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. Consider a particle that moves on a connected, undirected graph G with n vertices. At each step the particle goes from the current vertex to one of its neighbors, chosen uniformly at random. The cover time is the first time when the particle has visited all the vertices in the graph starting from a given vertex. In this paper, we present upper and lower bounds that relate the expected cover time for a graph to the eigenvalues of the Markov chain that describes the random walk above. An interesting consequence is that regular expander graphs have expected cover time \Theta(n log n). iii 1. Introduction. Consider a particle moving on an undirected graph G = (V; E) from vertex to vertex according to the following rule: the probability of a transition from vertex i, of degree d i , to vertex j is 1=d i if (i; j) 2 E, and 0 otherwise. This stochastic process is a Markov chain; it is called a random walk on the graph G. In this paper we derive upper and lower bounds on the expected cover...
The Juno2 ConstraintBased Drawing Editor
 Technical Report 131a, Digital Systems Research
, 1994
"... Constraints are an important enabling technology for interactive graphics applications. However, today's constraintbased systems are plagued by several limitations, and constraints have yet to live up to their potential. Juno2 is a constraintbased doubleview drawing editor that addresses so ..."
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Cited by 43 (4 self)
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Constraints are an important enabling technology for interactive graphics applications. However, today's constraintbased systems are plagued by several limitations, and constraints have yet to live up to their potential. Juno2 is a constraintbased doubleview drawing editor that addresses some of these limitations. Constraints in Juno2 are declarative, and they can include nonlinear functions and ordered pairs. Moreover, the Juno2 solver is not limited to acyclic constraint systems. Juno2 also includes a powerful extension language that allows users to define new constraints. The system demonstrates that fast constraint solving is possible with a highly extensible, fully declarative constraint language. The report describes what it is like to use Juno2, outlines the methods that Juno2 uses to solve constraints, and discusses its performance. Perspective Computers now handle the words in the documents that we write, and that is good: Revising, indexing, and formatting are lots...
SelfValidated Numerical Methods and Applications
, 1997
"... erical methods. We apologize to the reader for the length and verbosity of these notes but, like Pascal, 1 we didn't have the time to make them shorter. 1 "Je n'ai fait celleci plus longue que parce que je n'ai pas eu le loisir de la faire plus courte." Blaise Pascal, ..."
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Cited by 40 (0 self)
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erical methods. We apologize to the reader for the length and verbosity of these notes but, like Pascal, 1 we didn't have the time to make them shorter. 1 "Je n'ai fait celleci plus longue que parce que je n'ai pas eu le loisir de la faire plus courte." Blaise Pascal, Lettres Provinciales, XVI (1657). i ii Acknowledgements We thank the Organizing Committee of the 21 st Brazilian Mathematics Colloquium for the opportunity to present this course. We wish to thank Jo~ao Comba, who helped implement a prototype affine arithmetic package in Modula3, and Marcus Vinicius Andrade, who helped debug the C version and wrote an implicit surface raytracer based on it. Ronald van Iwaarden contributed an independent implementation of AA, and investigated its performance on branchandbound global optimization algorithms. Douglas Priest and Helmut Jarausch provided code and advice for rounding mode control. W
Curves and Surfaces in Geometric Modeling: Theory and Algorithms
, 2000
"... To my new daughter Mia, my wife Anne, ..."
Finding StaleValue Errors in Concurrent Programs
, 2002
"... Concurrent programs can suffer from many types of errors, not just the wellstudied problems of deadlocks and simple race conditions on variables. This paper addresses a kind of race condition that arises from reading a variable whose value is possibly outofdate. The paper introduces a simple te ..."
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Cited by 31 (0 self)
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Concurrent programs can suffer from many types of errors, not just the wellstudied problems of deadlocks and simple race conditions on variables. This paper addresses a kind of race condition that arises from reading a variable whose value is possibly outofdate. The paper introduces a simple technique for detecting such stale values, and reports on the encouraging experience with a compiletime checker that uses the technique.
Automatic camera calibration from a single manhattan image
 Eur. Conf. on Computer Vision (ECCV
, 2002
"... Abstract. We present a completely automatic method for obtaining the approximate calibration of a camera (alignment to a world frame and focal length) from a single image of an unknown scene, provided only that the scene satisfies a Manhattan world assumption. This assumption states that the imaged ..."
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Cited by 30 (3 self)
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Abstract. We present a completely automatic method for obtaining the approximate calibration of a camera (alignment to a world frame and focal length) from a single image of an unknown scene, provided only that the scene satisfies a Manhattan world assumption. This assumption states that the imaged scene contains three orthogonal, dominant directions, and is often satisfied by outdoor or indoor views of manmade structures and environments. The proposed method combines the calibration likelihood introduced in [5] with a stochastic search algorithm to obtain a MAP estimate of the camera’s focal length and alignment. Results on real images of indoor scenes are presented. The calibrations obtained are less accurate than those from standard methods employing a calibration pattern or multiple images. However, the outputs are certainly good enough for common vision tasks such as tracking. Moreover, the results are obtained without any user intervention, from a single image, and without use of a calibration pattern. 1
Reverse Engineering and System Renovation  An Annotated Bibliography 
 ACM Software Engineering Notes
, 1997
"... To facilitate research in the eld of reverse engineering and system renovation we have compiled an annotated bibliography. We put the contributions not only in alphabetical order but also grouped by topic so that readers focusing on a certain topic can read their annotations in the alphabetical l ..."
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Cited by 33 (14 self)
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To facilitate research in the eld of reverse engineering and system renovation we have compiled an annotated bibliography. We put the contributions not only in alphabetical order but also grouped by topic so that readers focusing on a certain topic can read their annotations in the alphabetical listing. We also compiled an annotated list of pointers to information about reverse engineering and system renovation that can be reached via Internet. For the sake of ease we also incorporated a brief introduction to the eld of reverse engineering. Key Words & Phrases: Reverse engineering, Annotated bibliography, System renovation 1991 CR Categories: A.2, D.2.2, D.2.7, D.2.m, K.6.3 note: The authors were all in part sponsored by bank ABN AMRO, software house DPFinance, and the Dutch Ministery of Economical Aairs via the Senter Project #ITU95017 "SOS Resolver". The last author was also supported by the Netherlands Computer Science Research Foundation (SION) with nancial support from the Netherlands Organization for Scientic Research (NWO), project Interactive tools for program understanding, 61233002. 1 Executive Summary There is a constant need for updating and renovating businesscritical software systems for many and divers reasons: business requirements change, technological infrastructure is modernized, the government changes laws, or the third millennium approaches, to mention a few. Therefore, that in the area of software engineering the subjects of reverse engineering and system renovation become more and more important. The interest in such subjects originates from the diculties that one encounters when attempting to maintain extremely large software systems. Such software systems are often called legacy systems, since it is a legacy of many dieren...
Annotation Inference for Modular Checkers
, 2000
"... This paper presents a general approach to annotation inference for a given static program checker. The approach reuses the checker as a subroutine. The approach has been used to implement annotation inference systems for two static program checkers, ESC/Java and rccjava. The paper describes the appr ..."
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Cited by 27 (6 self)
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This paper presents a general approach to annotation inference for a given static program checker. The approach reuses the checker as a subroutine. The approach has been used to implement annotation inference systems for two static program checkers, ESC/Java and rccjava. The paper describes the approach formally and shows how it applies to ESC.
Trading Space for Time in Undirected st Connectivity
 In Proceedings of the Twenty First Annual ACM Symposium on Theory of Computing
, 1991
"... Aleliunas et al. [1] posed the following question: "The reachability problem for undirected graphs can be solved in logspace and O.mn/ time [m is the number of edges and n is the number of vertices] by a probabilistic algorithm that simulates a random walk, or in linear time and space by a c ..."
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Cited by 23 (2 self)
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Aleliunas et al. [1] posed the following question: "The reachability problem for undirected graphs can be solved in logspace and O.mn/ time [m is the number of edges and n is the number of vertices] by a probabilistic algorithm that simulates a random walk, or in linear time and space by a conventional deterministic graph traversal algorithm. Is there a spectrum of timespace tradeoffs between these extremes?" We answer this question in the affirmative for graphs with a linear number of edges by presenting an algorithm that is faster than the random walk by a factor essentially proportional to the size of its workspace. For denser graphs, our algorithm is faster than the random walk but the speedup factor is smaller. v 1 Motivation and Results We consider the problem of st connectivity on an undirected graph (USTCON). Given a graph G with n vertices and m edges, and given two vertices s and t of G, we are to decide if s and t are in the same connected component. We are in...
The Mathematics of Perfect Shuffles
 ADVANCES IN APPLIED MATHEMATICS 4, 175 196 ( 1983)
, 1983
"... There are two ways to perfectly shuffle a deck of 2n cards. Both methods cut the deck in half and interlace perfectly. The out shuffle 0 leaves the original top card on top. The in shuffle I leaves the original top card second from the top. Applications to the design of computer networks and card tr ..."
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Cited by 23 (5 self)
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There are two ways to perfectly shuffle a deck of 2n cards. Both methods cut the deck in half and interlace perfectly. The out shuffle 0 leaves the original top card on top. The in shuffle I leaves the original top card second from the top. Applications to the design of computer networks and card tricks are reviewed. The main result is the determination of the group (I, 0) generated by the two shuffles, for all n. If 2 n is not a power of 2, and if 2n * 12,24, then (I, 0) has index 1,2, or 4 in the Weyl group B, (the group of all 2”n! signed n x n permutation matrices). If 2n = 2“, then (I, 0) is isomorphic to a semidirect product of Zi and Z,. When 2 n = 24, (I, 0) is isomorphic to a semidirect product of 2j ’ and M,,, the Mathieu group of degree 12. When 2n = 12, (I, 0) is isomorphic to a semidirect product of Zi and the group PGL(2,5) of all linear fractional transformations over GF(5).
Results 11  20
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133