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35
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 76 (32 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.
ExternalMemory Algorithms for Processing Line Segments in Geographic Information Systems
, 2007
"... In the design of algorithms for largescale applications it is essential to consider the problem of minimizing I/O communication. Geographical information systems (GIS) are good examples of such largescale applications as they frequently handle huge amounts of spatial data. In this paper we develop ..."
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Cited by 67 (25 self)
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In the design of algorithms for largescale applications it is essential to consider the problem of minimizing I/O communication. Geographical information systems (GIS) are good examples of such largescale applications as they frequently handle huge amounts of spatial data. In this paper we develop efficient externalmemory algorithms for a number of important problems involving line segments in the plane, including trapezoid decomposition, batched planar point location, triangulation, red–blue line segment intersection reporting, and general line segment intersection reporting. In GIS systems the first three problems are useful for rendering and modeling, and the latter two are frequently used for overlaying maps and extracting information from them.
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 (9 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...
Touring a sequence of polygons
 Proc. 35th ACM Sympos. Theory Comput
, 2003
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 37 (5 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Efficient ExternalMemory Data Structures and Applications
, 1996
"... In this thesis we study the Input/Output (I/O) complexity of largescale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer graphics, and design I/Oefficient algorithms for them. A general theme in our work is to design I/Oeffic ..."
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Cited by 37 (9 self)
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In this thesis we study the Input/Output (I/O) complexity of largescale problems arising e.g. in the areas of database systems, geographic information systems, VLSI design systems and computer graphics, and design I/Oefficient algorithms for them. A general theme in our work is to design I/Oefficient algorithms through the design of I/Oefficient data structures. One of our philosophies is to try to isolate all the I/O specific parts of an algorithm in the data structures, that is, to try to design I/O algorithms from internal memory algorithms by exchanging the data structures used in internal memory with their external memory counterparts. The results in the thesis include a technique for transforming an internal memory tree data structure into an external data structure which can be used in a batched dynamic setting, that is, a setting where we for example do not require that the result of a search operation is returned immediately. Using this technique we develop batched dynamic external versions of the (onedimensional) rangetree and the segmenttree and we develop an external priority queue. Following our general philosophy we show how these structures can be used in standard internal memory sorting algorithms
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 22 (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 Unified Approach to Dynamic Point Location, Ray Shooting, and Shortest Paths in Planar Maps
, 1992
"... We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map M with 7 ~ vertices, and apply it to the development of a unified dynamic data structure that supports pointlocation, rayshooting, and shortestpath queries in M. The space requirement i ..."
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Cited by 20 (6 self)
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We describe a new technique for dynamically maintaining the trapezoidal decomposition of a connected planar map M with 7 ~ vertices, and apply it to the development of a unified dynamic data structure that supports pointlocation, rayshooting, and shortestpath queries in M. The space requirement is O(nlog n). Pointlocation queries take time O(log 7~). Rayshooting and shortestpath queries take time O(log3 TZ) (plus O(k) time if the k edges of the shortest path are reported in addition to its length). Updates consist of insertions and deletions of vertices and edges, and take O(log3 n) time (amortized for vertex updates).
No Quadrangulation is Extremely Odd
, 1995
"... Given a set S of n points in the plane, a quadrangulation of S is a planar subdivision whose vertices are the points of S, whose outer face is the convex hull of S, and every face of the subdivision (except possibly the outer face) is a quadrilateral. We show that S admits a quadrangulation if a ..."
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Cited by 18 (3 self)
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Given a set S of n points in the plane, a quadrangulation of S is a planar subdivision whose vertices are the points of S, whose outer face is the convex hull of S, and every face of the subdivision (except possibly the outer face) is a quadrilateral. We show that S admits a quadrangulation if and only if S does not have an odd number of extreme points. If S admits a quadrangulation, we present an algorithm that computes a quadrangulation of S in O(n log n) time even in the presence of collinear points. If S does not admit a quadrangulation, then our algorithm can quadrangulate S with the addition of one extra point, which is optimal. We also provide an\Omega (n log n) time lower bound for the problem. Finally, our results imply that a kangulation of a set of points can be achieved with the addition of at most k \Gamma 3 extra points within the same time bound.
Dynamic and I/OEfficient Algorithms for Computational Geometry and Graph Problems: Theoretical and Experimental Results
, 1995
"... As most important applications today are largescale in nature, highperformance methods are becoming indispensable. Two promising computational paradigms for largescale applications are dynamic and I/Oefficient computations. We give efficient dynamic data structures for several fundamental proble ..."
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Cited by 17 (4 self)
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As most important applications today are largescale in nature, highperformance methods are becoming indispensable. Two promising computational paradigms for largescale applications are dynamic and I/Oefficient computations. We give efficient dynamic data structures for several fundamental problems in computational geometry, including point location, ray shooting, shortest path, and minimumlink path. We also develop a collection of new techniques for designing and analyzing I/Oefficient algorithms for graph problems, and illustrate how these techniques can be applied to a wide variety of specific problems, including list ranking, Euler tour, expressiontree evaluation, leastcommon ancestors, connected and biconnected components, minimum spanning forest, ear decomposition, topological sorting, reachability, graph drawing, and visibility representation. Finally, we present an extensive experimental study comparing the practical I/O efficiency of four algorithms for the orthogonal s...