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35
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 247 (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.
On Indexing Mobile Objects
, 1999
"... We show how to index mobile objects in one and two dimensions using efficient dynamic external memory data structures. The problem is motivated by real life applications in traffic monitoring, intelligent navigation and mobile communications domains. For the 1dimensional case, we give (i) a dynamic ..."
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Cited by 200 (14 self)
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We show how to index mobile objects in one and two dimensions using efficient dynamic external memory data structures. The problem is motivated by real life applications in traffic monitoring, intelligent navigation and mobile communications domains. For the 1dimensional case, we give (i) a dynamic, external memory algorithm with guaranteed worst case performance and linear space and (ii) a practical approximation algorithm also in the dynamic, external memory setting, which has linear space and expected logarithmic query time. We also give an algorithm with guaranteed logarithmic query time for a restricted version of the problem. We present extensions of our techniques to two dimensions. In addition we give a lower bound on the number of I/O's needed to answer the ddimensional problem. Initial experimental results and comparisons to traditional indexing approaches are also included. 1 Introduction Traditional database management systems assume that data stored in the database rem...
Fractional cascading: I. A data structuring technique
 Algorithmica
, 1986
"... Abstract. In computational geometry many search problems and range queries can be solved by performing an iterative search for the same key in separate ordered lists. In this paper we show that, if these ordered lists can be put in a onetoone correspondence with the nodes of a graph of degree d so ..."
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Cited by 156 (5 self)
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Abstract. In computational geometry many search problems and range queries can be solved by performing an iterative search for the same key in separate ordered lists. In this paper we show that, if these ordered lists can be put in a onetoone correspondence with the nodes of a graph of degree d so that the iterative search always proceeds along edges of that graph, then we can do much better than the obvious sequence of binary searches. Without expanding the storage by more than a constant factor, we can build a datastructure, called a fractional cascading structure, in which all original searches after the first can be carried out at only log d extra cost per search. Several results related to the dynamization of this structure are also presented. A companion paper gives numerous applications of this technique to geometric problems.
Filtering Search: A new approach to queryanswering
 SIAM J. Comput
, 1986
"... Abstract. We introduce a new technique for solving problems of the following form: preprocess a set ofobjects so that those satisfying a given property with respect to a query object canbe listed very effectively. Wellknown problems that fall into this category include range search, point enclosure ..."
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Cited by 106 (7 self)
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Abstract. We introduce a new technique for solving problems of the following form: preprocess a set ofobjects so that those satisfying a given property with respect to a query object canbe listed very effectively. Wellknown problems that fall into this category include range search, point enclosure, intersection, and nearneighbor problems. The approach which we take is very general and rests on a new concept called filtering search.We show on a number ofexamples how it can be used to improve the complexity ofknown algorithms and simplify their implementations as well. In particular, filtering search allows us to improve on the worstcase complexity ofthe best algorithms known so far for solving the problems mentioned above. Key words, computational geometry, database, data structures, filtering search, retrieval problems
Dynamic Trees and Dynamic Point Location
 In Proc. 23rd Annu. ACM Sympos. Theory Comput
, 1991
"... This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using ..."
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Cited by 46 (11 self)
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This paper describes new methods for maintaining a pointlocation data structure for a dynamicallychanging monotone subdivision S. The main approach is based on the maintenance of two interlaced spanning trees, one for S and one for the graphtheoretic planar dual of S. Queries are answered by using a centroid decomposition of the dual tree to drive searches in the primal tree. These trees are maintained via the linkcut trees structure of Sleator and Tarjan, leading to a scheme that achieves vertex insertion/deletion in O(log n) time, insertion/deletion of kedge monotone chains in O(log n + k) time, and answers queries in O(log 2 n) time, with O(n) space, where n is the current size of subdivision S. The techniques described also allow for the dual operations expand and contract to be implemented in O(log n) time, leading to an improved method for spatial pointlocation in a 3dimensional convex subdivision. In addition, the interlacedtree approach is applied to online pointlo...
RAY SHOOTING AND OTHER APPLICATIONS OF SPANNING TREES WITH LOW STABBING NUMBER
, 1992
"... This paper considers the following problem: Given a set G of n (possibly intersecting) line segments in the plane, prcproccss it so that, given a query ray p emanating from a point p, one can quickly compute the intersection point &(G, p) of p with a segment of G that lies nearest to p. The paper pr ..."
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Cited by 31 (11 self)
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This paper considers the following problem: Given a set G of n (possibly intersecting) line segments in the plane, prcproccss it so that, given a query ray p emanating from a point p, one can quickly compute the intersection point &(G, p) of p with a segment of G that lies nearest to p. The paper presents an algorithm that preproccsses G, in time 0 ( 3/2 log n), into a data structure of size O(nc(n) log4 n), so that for a query ray p, /,(, p) can be computed in time O(v/nc(ni log2 n), where w is a constant < 4.33 and a(n) is a functional inverse of Ackermannâ€™s function. If the given segments are nonintersecting, the storage goes down to O(n log3 n) and the query time becomes O(v/ log2 n). The main tool used is spanning trees (on the set of segment endpoints) with low stabbing number, i.e., with the property that no line intersects more than O(x/) edges of the tree. Such trees make it possible to obtain faster algorithms for several other problems, including implicit point location, polygon containment, and implicit hidden surface removal.
On Some Geometric Selection and Optimization Problems Via Sorted Matrices
, 1998
"... In this paper we apply the selection and optimization technique of Frederickson and Johnson to a number of geometric selection and optimization problems, some of which have previously been solved by parametric search, and provide efficient and simple algorithms. Our technique improves the solutions ..."
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Cited by 20 (2 self)
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In this paper we apply the selection and optimization technique of Frederickson and Johnson to a number of geometric selection and optimization problems, some of which have previously been solved by parametric search, and provide efficient and simple algorithms. Our technique improves the solutions obtained by parametric search by a log n factor. For example, we apply the technique to the twoline center problem, where we want to find two strips that cover a given set S of n points in the plane, so as to minimize the width of the largest of the two strips. Key words: computational geometry, algorithm, selection, optimization, twoline center. A version of this paper appeared in Fourth Workshop on Algorthms and Data Structures, S.G. Akl, F. Dehne, J. Sack and N. Santoro, editors, Lecture Notes in Computer Science 955, SpringerVerlag, pp. 2635. Work by K. Kedem has been supported by a grant from the U.S.Israeli Binational Science Foundation, and by a grant from the Israel Science ...
Methods for Achieving Fast Query Times in Point Location Data Structures
, 1997
"... Given a collection S of n line segments in the plane, the planar point location problem is to construct a data structure that can efficiently determine for a given query point p the first segment(s) in S intersected by vertical rays emanating out from p. It is well known that linearspace data struc ..."
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Cited by 20 (1 self)
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Given a collection S of n line segments in the plane, the planar point location problem is to construct a data structure that can efficiently determine for a given query point p the first segment(s) in S intersected by vertical rays emanating out from p. It is well known that linearspace data structures can be constructed so as to achieve O(log n) query times. But applications, such as those common in geographic information systems, motivate a reexamination of this problem with the goal of improving query times further while also simplifying the methods needed to achieve such query times. In this paper we perform such a reexamination, focusing on the issues that arise in three different classes of pointlocation query sequences: ffl sequences that are reasonably uniform spatially and temporally (in which case the constant factors in the query times become critical), ffl sequences that are nonuniform spatially or temporally (in which case one desires data structures that adapt to s...
A simple entropybased algorithm for planar point location
 In Proceedings of the Twelfth Annual ACMSIAM Symposium on Discrete Algorithms
, 2001
"... Abstract Given a planar polygonal subdivision S, point location involves preprocessing this subdivisioninto a data structure so that given any query point q, the cell of the subdivision containing qcan be determined efficiently. Suppose that for each cell z in the subdivision, the probability pz tha ..."
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Cited by 20 (5 self)
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Abstract Given a planar polygonal subdivision S, point location involves preprocessing this subdivisioninto a data structure so that given any query point q, the cell of the subdivision containing qcan be determined efficiently. Suppose that for each cell z in the subdivision, the probability pz that a query point lies within this cell is also given. The goal is to design the data structureto minimize the average search time. This problem has been considered before, but existing
Nearly Optimal ExpectedCase Planar Point Location
"... We consider the planar point location problem from the perspective of expected search time. We are given a planar polygonal subdivision S and for each polygon of the subdivision the probability that a query point lies within this polygon. The goal is to compute a search structure to determine which ..."
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Cited by 17 (5 self)
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We consider the planar point location problem from the perspective of expected search time. We are given a planar polygonal subdivision S and for each polygon of the subdivision the probability that a query point lies within this polygon. The goal is to compute a search structure to determine which cell of the subdivision contains a given query point, so as to minimize the expected search time. This is a generalization of the classical problem of computing an optimal binary search tree for onedimensional keys. In the onedimensional case it has long been known that the entropy H of the distribution is the dominant term in the lower bound on the expectedcase search time, and further there exist search trees achieving expected search times of at most H + 2. Prior to this work, there has been no known structure for planar point location with an expected search time better than 2H, and this result required strong assumptions on the nature of the query point distribution. Here we present a data structure whose expected search time is nearly equal to the entropy lower bound, namely H + o(H). The result holds for any polygonal subdivision in which the number of sides of each of the polygonal cells is bounded, and there are no assumptions on the query distribution within each cell. We extend these results to subdivisions with convex cells, assuming a uniform query distribution within each cell.