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Purely Functional, RealTime Deques with Catenation
 Journal of the ACM
, 1999
"... We describe an efficient, purely functional implementation of deques with catenation. In addition to being an intriguing problem in its own right, finding a purely functional implementation of catenable deques is required to add certain sophisticated programming constructs to functional programming ..."
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Cited by 17 (2 self)
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We describe an efficient, purely functional implementation of deques with catenation. In addition to being an intriguing problem in its own right, finding a purely functional implementation of catenable deques is required to add certain sophisticated programming constructs to functional programming languages. Our solution has a worstcase running time of O(1) for each push, pop, inject, eject and catenation. The best previously known solution has an O(log k) time bound for the k deque operation. Our solution is not only faster but simpler. A key idea used in our result is an algorithmic technique related to the redundant digital representations used to avoid carry propagation in binary counting.
Confluently Persistent Deques via DataStructural Bootstrapping
 J. of Algorithms
, 1993
"... We introduce datastructural bootstrapping, a technique to design data structures recursively, and use it to design confluently persistent deques. Our data structure requires O(log 3 k) worstcase time and space per deletion, where k is the total number of deque operations, and constant worstcase t ..."
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Cited by 15 (4 self)
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We introduce datastructural bootstrapping, a technique to design data structures recursively, and use it to design confluently persistent deques. Our data structure requires O(log 3 k) worstcase time and space per deletion, where k is the total number of deque operations, and constant worstcase time and space for other operations. Further, the data structure allows a purely functional implementation, with no side effects. This improves a previous result of Driscoll, Sleator, and Tarjan. 1 An extended abstract of this paper was presented at the 4th ACMSIAM Symposium on Discrete Algorithms, 1993. 2 Supported by a Fannie and John Hertz Foundation fellowship, National Science Foundation Grant No. CCR8920505, and the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) under NSFSTC8809648. 3 Also affiliated with NEC Research Institute, 4 Independence Way, Princeton, NJ 08540. Research at Princeton University partially supported by the National Science Foundatio...
A LearningBased PredictionandVerification Segmentation Scheme for Hand Sign Image Sequences
, 1995
"... This paper presents a predictionandverification segmentation scheme using attention images from multiple fixations. The scheme has two major components: (a) a hierarchical quasiVoronoi diagram which organizes training attention images for prediction of the segmentation masks; (b) a learningba ..."
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Cited by 14 (3 self)
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This paper presents a predictionandverification segmentation scheme using attention images from multiple fixations. The scheme has two major components: (a) a hierarchical quasiVoronoi diagram which organizes training attention images for prediction of the segmentation masks; (b) a learningbased function approximation scheme to verify the segmentation result. A major advantage of this scheme is that it can handle a large number of different deformable objects presented in complex backgrounds. The scheme is also relatively efficient since the segmentation is guided by the past knowledge through a predictionandverification scheme. The system was tested to segment hands in sequences of intensity images, where each sequence represents a hand sign in American Sign Language. The experimental result showed a 95% correct segmentation rate with a 3% false rejection rate. Categories: 2D segmentation, hand sign recognition, visual learning, nearest neighbor, and feature derivatio...
Making Data Structures Confluently Persistent
, 2001
"... We address a longstanding open problem of [10, 9], and present a general transformation that transforms any pointer based data structure to be confluently persistent. Such transformations for fully persistent data structures are given in [10], greatly improving the performance compared to the naive ..."
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Cited by 12 (0 self)
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We address a longstanding open problem of [10, 9], and present a general transformation that transforms any pointer based data structure to be confluently persistent. Such transformations for fully persistent data structures are given in [10], greatly improving the performance compared to the naive scheme of simply copying the inputs. Unlike fully persistent data structures, where both the naive scheme and the fully persistent scheme of [10] are feasible, we show that the naive scheme for confluently persistent data structures is itself infeasible (requires exponential space and time). Thus, prior to this paper there was no feasible method for implementing confluently persistent data structures at all. Our methods give an exponential reduction in space and time compared to the naive method, placing confluently persistent data structures in the realm of possibility.
Nearest Neighbor Search in Multidimensional Spaces
, 1999
"... The Nearest Neighbor Search problem is defined as follows: given a set P of n points, preprocess the points so as to efficiently answer queries that require finding the closest point in P to a query point q. If we are willing to settle for a point that is almost as close as the nearest neighbor, t ..."
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The Nearest Neighbor Search problem is defined as follows: given a set P of n points, preprocess the points so as to efficiently answer queries that require finding the closest point in P to a query point q. If we are willing to settle for a point that is almost as close as the nearest neighbor, then we can relax the problem to the approximate Nearest Neighbor Search. Nearest Neighbor Search (exact or approximate) is an integral component in a wide range of applications that include multimedia databases, computational biology, data mining, and information retrieval. The common thread in all these applications is similarity search: given a database of objects, we want to return the object in the database that is most similar to a query object. The objects are mapped onto points in a high dimensional metric space , and similarity search reduces to a nearest neighbor search. The dimension of the underlying space may be in the order of a few hundreds, or thousands; therefore, we r...
Computational Geometry
 in optimization 2.5D and 3D NC surface machining. Computers in Industry
, 1996
"... Introduction Computational geometry evolves from the classical discipline of design and analysis of algorithms, and has received a great deal of attention in the last two decades since its inception in 1975 by M. Shamos[108]. It is concerned with the computational complexity of geometric problems t ..."
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Cited by 11 (0 self)
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Introduction Computational geometry evolves from the classical discipline of design and analysis of algorithms, and has received a great deal of attention in the last two decades since its inception in 1975 by M. Shamos[108]. It is concerned with the computational complexity of geometric problems that arise in various disciplines such as pattern recognition, computer graphics, computer vision, robotics, VLSI layout, operations research, statistics, etc. In contrast with the classical approach to proving mathematical theorems about geometryrelated problems, this discipline emphasizes the computational aspect of these problems and attempts to exploit the underlying geometric properties possible, e.g., the metric space, to derive efficient algorithmic solutions. The classical theorem, for instance, that a set S is convex if and only if for any 0 ff 1 the convex combination ffp + (1 \Gamma<F
Range Searching and Point Location among Fat Objects
 Journal of Algorithms
, 1994
"... We present a data structure that can store a set of disjoint fat objects in dspace such that point location and boundedsize range searching with arbitrarilyshaped ranges can be performed efficiently. The structure can deal with either arbitrary (fat) convex objects or nonconvex polytopes. The m ..."
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Cited by 11 (0 self)
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We present a data structure that can store a set of disjoint fat objects in dspace such that point location and boundedsize range searching with arbitrarilyshaped ranges can be performed efficiently. The structure can deal with either arbitrary (fat) convex objects or nonconvex polytopes. The multipurpose data structure supports point location and range searching queries in time O(log d\Gamma1 n) and requires O(n log d\Gamma1 n) storage, after O(n log d\Gamma1 n log log n) preprocessing. The data structure and query algorithm are rather simple. 1 Introduction Fatness turns out to be an interesting phenomenon in computational geometry. Several papers present surprising combinatorial complexity reductions [3, 15, 22, 26, 32] and efficiency gains for algorithms [1, 4, 19, 28, 33] if the objects under consideration have a certain fatness. Fat objects are compact to some extent, rather than long and thin. Fatness is a realistic assumption, since in many practical instances of ...
Robust Proximity Queries in Implicit Voronoi Diagrams
 IN PROC. 8TH CANAD. CONF. COMPUT. GEOM
, 1996
"... In the context of methodologies intended to confer robustness to geometric algorithms, we elaborate on the exact computation paradigm and formalize the notion of degree of a geometric algorithm, as a worstcase quantification of the precision (number of bits) to which arithmetic calculation have ..."
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In the context of methodologies intended to confer robustness to geometric algorithms, we elaborate on the exact computation paradigm and formalize the notion of degree of a geometric algorithm, as a worstcase quantification of the precision (number of bits) to which arithmetic calculation have to be executed in order to guarantee topological correctness. We also propose a formalism for the expeditious evaluation of algorithmic degree. As an application of this paradigm and an illustration of our general approach, we consider the important classical problem of proximity queries in 2 and 3 dimensions, and develop a new technique for the efficient and robust execution of such queries based on an implicit representation of Voronoi diagrams. Our new technique gives both low degree and fast query time, and for 2D queries is optimal with respect to both cost measures of the paradigm, asymptotic number of operations and arithmetic degree.
Optimal Cooperative Search In Fractional Cascaded Data Structures
, 1995
"... Fractional cascading is a technique designed to allow efficient sequential search in a graph with catalogs of total size n. The search consists of locating a key in the catalogs along a path. In this paper we show how to preprocess a variety of fractional cascaded data structures whose underlying ..."
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Fractional cascading is a technique designed to allow efficient sequential search in a graph with catalogs of total size n. The search consists of locating a key in the catalogs along a path. In this paper we show how to preprocess a variety of fractional cascaded data structures whose underlying graph is a tree so that searching can be done efficiently in parallel. The preprocessing takes O(log n) time with n/log n processors on an EREW PRAM. For a balanced binary tree cooperative search along roottoleaf paths can be done in O((logn)/logp) time using p processors on a CREW PRAM.
DataStructural Bootstrapping And Catenable Deques
, 1993
"... The list is a fundamental data structure. It stores a linearly ordered collection of elements and allows access only to the front and rear elements of the list. Catenation can be applied to lists, unifying the rear of one list with the front of another. Absent other requirements, the basic list oper ..."
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Cited by 5 (0 self)
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The list is a fundamental data structure. It stores a linearly ordered collection of elements and allows access only to the front and rear elements of the list. Catenation can be applied to lists, unifying the rear of one list with the front of another. Absent other requirements, the basic list operations, including catenation, have straightforward implementations. If the list has certain secondary properties, however, the operations, particularly catenation, become more difficult. Nondestructive lists