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13
Making Data Structures Persistent
, 1989
"... This paper is a study of persistence in data structures. Ordinary data structures are ephemeral in the sense that a change to the structure destroys the old version, leaving only the new version available for use. In contrast, a persistent structure allows access to any version, old or new, at any t ..."
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Cited by 250 (6 self)
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This paper is a study of persistence in data structures. Ordinary data structures are ephemeral in the sense that a change to the structure destroys the old version, leaving only the new version available for use. In contrast, a persistent structure allows access to any version, old or new, at any time. We develop simple, systematic, and effiient techniques for making linked data structures persistent. We use our techniques to devise persistent forms of binary search trees with logarithmic access, insertion, and deletion times and O(1) space bounds for insertion and deletion.
An optimal algorithm for intersecting threedimensional convex polyhedra
 SIAM J. Comput
, 1992
"... Abstract. This paper describes a lineartime algorithm for computing the intersection of two convex polyhedra in 3space. Applications of this result to computing intersections, convex hulls, and Voronoi diagrams are also given. Key words, computational geometry, convex polyhedra AMS(MOS) subject cl ..."
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Cited by 62 (4 self)
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Abstract. This paper describes a lineartime algorithm for computing the intersection of two convex polyhedra in 3space. Applications of this result to computing intersections, convex hulls, and Voronoi diagrams are also given. Key words, computational geometry, convex polyhedra AMS(MOS) subject classifications. 68Q25, 68H05 1. Introduction. Giventwo
Intersection of Convex Objects in Two and Three Dimensions
, 1987
"... One of the basic geometric operations involves determining whether a pair of convex objects intersect. This problem is well understood in a model of computation in which the objects are given as input and their intersection is returned as output. For many applications, however, it may be assumed tha ..."
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Cited by 49 (3 self)
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One of the basic geometric operations involves determining whether a pair of convex objects intersect. This problem is well understood in a model of computation in which the objects are given as input and their intersection is returned as output. For many applications, however, it may be assumed that the objects already exist within the computer and that the only output desired is a single piece of data giving a common point if the objects intersect or reporting no intersection if they are disjoint. For this problem, none of the previous lower bounds are valid and algorithms are proposed requiring sublinear time for their solution in two and three dimensions.
Computational geometry  a survey
 IEEE TRANSACTIONS ON COMPUTERS
, 1984
"... We survey the state of the art of computational geometry, a discipline that deals with the complexity of geometric problems within the framework of the analysis ofalgorithms. This newly emerged area of activities has found numerous applications in various other disciplines, such as computeraided de ..."
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Cited by 19 (3 self)
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We survey the state of the art of computational geometry, a discipline that deals with the complexity of geometric problems within the framework of the analysis ofalgorithms. This newly emerged area of activities has found numerous applications in various other disciplines, such as computeraided design, computer graphics, operations research, pattern recognition, robotics, and statistics. Five major problem areasconvex hulls, intersections, searching, proximity, and combinatorial optimizationsare discussed. Seven algorithmic techniques incremental construction, planesweep, locus, divideandconquer, geometric transformation, pruneandsearch, and dynamizationare each illustrated with an example.Acollection of problem transformations to establish lower bounds for geometric problems in the algebraic computation/decision model is also included.
Purely Functional Representations of Catenable Sorted Lists.
 In Proceedings of the 28th Annual ACM Symposium on Theory of Computing
, 1996
"... The power of purely functional programming in the construction of data structures has received much attention, not only because functional languages have many desirable properties, but because structures built purely functionally are automatically fully persistent: any and all versions of a structur ..."
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Cited by 16 (5 self)
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The power of purely functional programming in the construction of data structures has received much attention, not only because functional languages have many desirable properties, but because structures built purely functionally are automatically fully persistent: any and all versions of a structure can coexist indefinitely. Recent results illustrate the surprising power of pure functionality. One such result was the development of a representation of doubleended queues with catenation that supports all operations, including catenation, in worstcase constant time [19].
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...
NREVERSAL of Fortune  The Thermodynamics of Garbage Collection
 In ACM Sigplan Notices
, 1977
"... The need to reverse a computation arises in many contextsdebugging, editor undoing, optimistic concurrency undoing, speculative computation undoing, trace scheduling, exception handling undoing, database recovery, optimistic discrete event simulations, subjunctive computing, etc. The need to anal ..."
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Cited by 14 (0 self)
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The need to reverse a computation arises in many contextsdebugging, editor undoing, optimistic concurrency undoing, speculative computation undoing, trace scheduling, exception handling undoing, database recovery, optimistic discrete event simulations, subjunctive computing, etc. The need to analyze a reversed computation arises in the context of static analysisliveness analysis, strictness analysis, type inference, etc. Traditional means for restoring a computation to a previous state involve checkpoints; checkpoints require time to copy, as well as space to store, the copied material. Traditional reverse abstract interpretation produces relatively poor information due to its inability to guess the previous values of assignedto variables. We propose an abstract computer model and a programming languageYLispwhose primitive operations are injective and hence reversible, thus allowing arbitrary undoing without the overheads of checkpointing. Such a computer can be built from reversible conservative logic circuits, with the serendipitous advantage of dissipating far less heat than traditional Boolean AND/OR/NOT circuits. Unlike functional languages, which have one "state " for all times, YLisp has at all times one "state", with unique predecessor and successor states. Compiling into a reversible pseudocode can have benefits even when targeting a traditional computer. Certain optimizations, e.g., updateinplace, and compiletime garbage collection may be more easily performed, because the
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 13 (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.
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 10 (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.
Persistent data structures
 IN HANDBOOK ON DATA STRUCTURES AND APPLICATIONS, CRC PRESS 2001, DINESH MEHTA AND SARTAJ SAHNI (EDITORS) BOROUJERDI, A., AND MORET, B.M.E., "PERSISTENCY IN COMPUTATIONAL GEOMETRY," PROC. 7TH CANADIAN CONF. COMP. GEOMETRY, QUEBEC
, 1995
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