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99
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 217 (16 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...
Ray shooting and parametric search
, 1993
"... Efficient algorithms for the ray shooting problem are presented: Given a collection F of objects in d, build a data structure so that, for a query ray, the first object of F hit by the ray can be quickly determined. Using the parametric search technique, this problem is reduced to the segment emptin ..."
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Cited by 126 (22 self)
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Efficient algorithms for the ray shooting problem are presented: Given a collection F of objects in d, build a data structure so that, for a query ray, the first object of F hit by the ray can be quickly determined. Using the parametric search technique, this problem is reduced to the segment emptiness problem. For various ray shooting problems, space/querytime tradeoffs of the following type are achieved: For some integer b and a parameter m (n _< m < n b) the queries are answered in time O((n/m /b) log <) n), with O(m!+) space and preprocessing time (t> 0 is arbitrarily small but fixed constant), b Ld/2J is obtained for ray shooting in a convex dpolytope defined as an intersection of n half spaces, b d for an arrangement of n hyperplanes in d, and b 3 for an arrangement of n half planes in 3. This approach also yields fast procedures for finding the first k objects hit by a query ray, for searching nearest and farthest neighbors, and for the hidden surface removal. All the data structures can be maintained dynamically in amortized time O (m + / n) per insert/delete operation.
Applications of parametric searching in geometric optimization
 J. Algorithms
, 1994
"... z Sivan Toledo x ..."
External Memory Data Structures
, 2001
"... In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynami ..."
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Cited by 73 (31 self)
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In many massive dataset applications the data must be stored in space and query efficient data structures on external storage devices. Often the data needs to be changed dynamically. In this chapter we discuss recent advances in the development of provably worstcase efficient external memory dynamic data structures. We also briefly discuss some of the most popular external data structures used in practice.
Efficient Searching with Linear Constraints (Extended Abstract)
"... We show how to preprocess a set S of points in R d to get an external memory data structure that efficiently supports linearconstraint queries. Each query is in the form of a linear constraint a \Delta x b; the data structure must report all the points of S that satisfy the query. Our goal i ..."
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Cited by 56 (16 self)
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We show how to preprocess a set S of points in R d to get an external memory data structure that efficiently supports linearconstraint queries. Each query is in the form of a linear constraint a \Delta x b; the data structure must report all the points of S that satisfy the query. Our goal is to minimize the number of disk blocks required to store the data structure and the number of disk accesses (I/Os) required to answer a query. For d = 2, we present the first nearlinear size data structures that can answer linearconstraint queries using an optimal number of I/Os. We also present a linearsize data structure that can answer queries efficiently in the worst case. We combine these two approaches to obtain tradeoffs between space and query time. Finally, we show that some of our techniques extend to higher dimensions d.
Geometric Applications of a Randomized Optimization Technique
, 1999
"... We propose a simple, general, randomized technique to reduce certain geometric optimization problems to their corresponding decision problems. These reductions increase the expected time complexity by only a constant factor and eliminate extra logarithmic factors in previous, often more complicated ..."
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Cited by 54 (11 self)
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We propose a simple, general, randomized technique to reduce certain geometric optimization problems to their corresponding decision problems. These reductions increase the expected time complexity by only a constant factor and eliminate extra logarithmic factors in previous, often more complicated, deterministic approaches (such as parametric searching). Faster algorithms are thus obtained for a variety of problems in computational geometry: finding minimal kpoint subsets, matching point sets under translation, computing rectilinear pcenters and discrete 1centers, and solving linear programs with k violations.
Geometric Range Searching
, 1994
"... In geometric range searching, algorithmic problems of the following type are considered: Given an npoint set P in the plane, build a data structure so that, given a query triangle R, the number of points of P lying in R can be determined quickly. Problems of this type are of crucial importance in c ..."
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Cited by 54 (3 self)
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In geometric range searching, algorithmic problems of the following type are considered: Given an npoint set P in the plane, build a data structure so that, given a query triangle R, the number of points of P lying in R can be determined quickly. Problems of this type are of crucial importance in computational geometry, as they can be used as subroutines in many seemingly unrelated algorithms. We present a survey of results and main techniques in this area.
Efficient Image Retrieval through Vantage Objects
 Pattern Recognition
, 1999
"... We describe a new indexing structure for general image retrieval that relies solely on a distance function giving the similarity between two images. For each image object in the database, its distance to a set of m predetermined vantage objects is calculated; the mvector of these distances specifie ..."
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Cited by 53 (9 self)
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We describe a new indexing structure for general image retrieval that relies solely on a distance function giving the similarity between two images. For each image object in the database, its distance to a set of m predetermined vantage objects is calculated; the mvector of these distances specifies a point in the mdimensional vantage space. The database objects that are similar (in terms of the distance function) to a given query object can be determined by means of an efficient nearestneighbor search on these points. We demonstrate the viability of our approach through experimental results obtained with a database of about 48,000 hieroglyphic polylines.