Y. Chiang and R. Tamassia, "Dynamic Algorithms in Computational Geometry," Brown University Deptartment of Computer Science technical report CS-91-24, 1991.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....geometric optimization and measure problems and study their worst case complexities in the dynamic setting, and try to gain a better understanding into generally what types of problems admit nontrivial dynamization results. The importance of dynamic computational geometry was realized long ago [10], and while there have been many fundamental results in the area, our current knowledge is still limited. Dynamic data structures for all kinds of problems reducible to range searching [1] including linear convex programming, are known. A class of decomposable query problems [5] has been ....

Y.-J. Chiang and R. Tamassia, Dynamic algorithms in computational geometry, Proc. of the IEEE, 80:1412-1434, 1992.

....types are mixed in the request stream, and we would like a fast guaranteed worst case response time. The machine servicing the requests may be either a sequential or parallel machine. While incremen tal versions of many graph problems (for example [9, 11, 20] and geometry problems (for example [1, 6, 21]) have been studied, very little has been done in incremental versions of algebraic problems. Two notable exceptions are the incremental maintenance of prefix sums studied by Fredman [10] and the incremental maintenance and evaluation of size n algebraic expressions studied by Frederickson [12] ....

Y. Chiang and R. Tamassia, "Dynamic Algorithms in Computational Geometry," Technical Report CS-91-24, Brown University Department of Computer Science, 1991.

....[9] applies only to range counting and not to range sum. Furthermore, the data structure is rather complex to implement in practice. Note that the ECDF tree and the range tree are both static and internal memory structures. To dynamize a static data structure some standard techniques can be used [12]. For example, the global rebuilding [24] or the logarithmic method [8] To externalize an internal memory data structure, a widely used method is to augment it with block access capabilities [34] Range Sum for Data Cubes and Point Data. The data cube range sum problem addresses the following ....

Y. Chiang and R. Tamassia, \Dynamic Algorithms in Computational Geometry", Proc. of the IEEE, Special Issue on Computational Geometry, G. Toussaint (Ed.), 80(9), 1992.

....O(log n) time. Their data structure does not provide an explicit representation of the convex hull in terms of a search tree with the points on the convex hull. They can reduce the space usage to O(n) if the queries are also part of the off line information. In a survey paper Chiang and Tamassia [CT92] regard dynamic planar convex hull as one of the two most important problems in dynamic computational geometry. More precisely they ask, whether a data structure exists that has O(log n) update and query times. Chan in 1999 [Cha99a, Cha01] proposes a construction for the fully dynamic problem ....

Yi-Jen Chiang and Roberto Tamassia. Dynamic algorithms in computational geometry. Proceedings of the IEEE, 80(9):1412--1434, September 1992.

....the red blue segment intersection problem where all red and all blue segments are connected. 1 Introduction The problem of maintaining the convex hull of a set of points in the plane under the insertion and deletion of points is one of the foremost important problems in computational geometry [6, 10]. A dynamic data structure for maintaining the convex hull of a point set has numerous applications, e.g. in algorithms solving the k level problem [7] and the red blue segment intersection problem where all red and all blue segments are connected [1] For further applications see [4] Overmars ....

Y.-J. Chiang and R. Tamassia. Dynamic algorithms in computational geometry. Proceedings of the IEEE, Special Issue on Computational Geometry, 80(9):1412--1434, 1992.

....Their data structure does not provide an explicit representation of the convex hull. They can reduce the space usage to O(n) if the queries are also part of the o# line information. They consider the online version of the problem a long standing open problem. In a survey paper Chiang and Tamassia [CT92] regard dynamic planar convex hull as one of the two most important problems in dynamic computational geometry. More precisely they ask, whether a data structure exists that has O(log n) update and query times. In a technical report Kapoor [Kap95] presents a data structure that is a variation of ....

Y.-J. Chiang and R. Tamassia, Dynamic algorithms in computational geometry, Proceedings of the IEEE 80 (1992), no. 9, 1412--1434.

....dynamic k dimensional range searching on relational database attributes x 1 ; x k generalizes 1dimensional range searching to k attributes, with range searching on k dimensional intervals. Many efficient algorithms exist for 2 dimensional range searching and its special cases (see [ChT] for a detailed survey) Most of these algorithms are not efficient when mapped to secondary storage. However, the practical need for good I O support has led to the development of a large number of external data structures, which do not have good theoretical worst case bounds but have good ....

Y.-J. Chiang and R. Tamassia, "Dynamic Algorithms in Computational Geometry," Proceedings of IEEE, Special Issue on Computational Geometry 80(9) (1992), 362--381.

....consists of polygons that are monotone (so no straight line crosses any polygon more than twice) Preparata and Tamassia [16] give an algorithm that runs in time O(log per operation. Several other dynamic algorithms for this and other types of subdivisions have been found since, see [4] for a survey. 4 To prove a lower bound for this problem we construct a monotone subdivision from the signed prefix sum instance y 2 f0; Sigma1g . This is easier drawn than explained formally; Fig. 1 shows the subdivision corresponding to y = 0, 0, 1, 1, Gamma1, 0, 1 ,0) There are 2 ....

Yi-Jen Chiang and Roberto Tamassia. Dynamic algorithms in computational geometry. Technical Report CS-91-24, Dept. of Comp. Sc., Brown University, 1991.

....return yes if and only if x is in the same polygon as the origin. Our operations are very weak, since we want to prove a useful lower bound. Efficient algorithms are known for more powerful operations that return the name of a queried polygon, and insert and delete (chains of) edges, see [7, 14, 59]. Theorem 6 Every algorithm for dynamic planar point location in monotone subdivisions uses Omega Gammaes n= log log n) steps per operation. Proof. To prove a lower bound for this problem we construct a monotone subdivision from the instance x 2 f0; Sigma1g that is similar to the upward ....

Yi-Jen Chiang and Roberto Tamassia. Dynamic algorithms in Computational Geometry. Technical Report CS-91-24, Dept. of Comp. Sc., Brown University, 1991.

....and updating on multi dimensional tree can be performed as usual. In addition, we demonstrate how a multi dimensional minima searching problem can be solved recursively by decreasing the dimensionality. 1 Introduction The minima searching problem, an important computational geometry problem [CT92][Cha94] is to determine whether a k dimensional point is minimal among a set of points. Let S be a set of points :G .B0 CM r; DB 85C5:wLZ NDs0F. ld 3 1m El5 Bg3XBg3X1 9)3X7O8 5f2J pJs9)3X l96, Department of Information Engineering, University of Tokyo. 8U 69 , Ip;T 5 M, El5 Bg3XBg3X1 ....

Chiang,Y.J. and Tamassia, T. : Dynamic Algorithms in Computational Geometry. Proceedings of the IEEE, Special Issue on Computational Geometry, Vol. 80, No. 9(1992), pp.1412-1434.

....deal of work on decomposable searching problems. They were introduced by Bentley [8] for dynamizing static data structures. The initial goal was to support insertions with low amortized times, without a ecting much of the query eciency. Other dynamization techniques were subsequently given (see [11, 33] for many references to the literature) The main idea behind these techniques is to partition a big data structure into a collection of small data structures, called blocks, and to tune properly the number of blocks in order to obtain a good tradeo between queries and updates. Later on, van ....

....for windowing problems in computer graphics and databases, and in several cases it was rather dicult to keep them balanced [35, 40] In contrast, our cross tree can be easily kept balanced. Many other powerful data structures for range queries were devised subsequently and we refer the reader to [11] for a comprehensive survey on this topic and a list of references. Recently, some elegant data structures [5, 24, 36, 38, 42, 43] were devised to support fast range queries in external memory, and Arge et al. 4] have dealt with some decomposable problems in external memory. However, none of ....

Y.-J. Chiang and R. Tamassia. Dynamic algorithms in computational geometry. Proceedings of the IEEE, Special issue on Computational Geometry, G. Toussaint, ed., 80 (1992) 1412-1434.

....applies only to rangecounting and not to range sum. Furthermore, the data structure is rather complex to implement in practice. Note that the ECDF tree and the range tree are both static and internal memory structures. To dynamize a static data structure some standard techniques can be used [CT92]. For example, the global rebuilding ( Ove83] or the logarithmic method ( BS80] To externalize an internal memory data structure, a widely used method is to augment it with block access capabilities [Vit01] Range Sum for Data Cubes. The data cube range sum problem addresses the following ....

Y. Chiang and R. Tamassia, "Dynamic Algorithms in Computational Geometry", Proc. of the IEEE, Special Issue on Computational Geometry, G. Toussaint (Ed.), 80(9), pp. 1412-1434, 1992.

....geometric optimization and measure problems and study their worst case complexities in the dynamic setting, and try to gain a better understanding into generally what types of problems admit nontrivial dynamization results. The importance of dynamic computational geometry was realized long ago [10], and while there have been many fundamental results in the area, our current knowledge is still limited. Dynamic data structures for all kinds of problems reducible to range searching [1] including linear convex programming, are known. A class of decomposable query problems [5] has been ....

Y.-J. Chiang and R. Tamassia. Dynamic algorithms in computational geometry. Proc. of the IEEE, 80:1412-1434, 1992.

....external memory has been the subject of much research. Many elegant data structures like the range tree [24] the priority search tree [89] the segment tree [23] and the interval tree [53, 54] have been proposed for use in main memory for 2 dimensional range searching and its special cases (see [43] for a detailed survey) Most of these structures are not efficient when mapped to external memory. However, the practical need for I O support has led to the development of a large number of external data structures that do not have good theoretical worst case update and query I O bounds, but do ....

Y.-J. Chiang and R. Tamassia. Dynamic algorithms in computational geometry. Proceedings of IEEE, Special Issue on Computational Geometry, 80(9):362--381, 1992.

....external memory has been the subject of much research. Many elegant data structures like the range tree [7] the priority search tree [27] the segment tree [6] and the interval tree [14, 15] have been proposed for use in main memory for 2 dimensional range searching and its special cases (see [11] for a detailed survey) Most of these structures are not efficient when mapped to external memory. However, the practical need for I O support has led to the development of a large number of external data structures that do not have good theoretical worstcase update and query I O bounds, but do ....

Y.-J. Chiang and R. Tamassia. Dynamic algorithms in computational geometry. Proceedings of IEEE, Special Issue on Computational Geometry, 80(9):362--381, 1992.

.... of operations by paying a logarithmic overhead in the query time [109] These techniques work even if the sequence of insertions and queries is not known in advance, but the deletion time of a point is known when it is inserted [99] see also [233] See the survey paper by Chiang and Tamassia [83] for a more detailed review of dynamic geometric data structures. 6 Intersection Searching A general intersection searching problem can be formulated as follows. Given a set S of objects in R d , a semigroup (S; and a weight function w : S S, we wish to preprocess S into a data structure ....

Y.-J. Chiang and R. Tamassia, Dynamic algorithms in computational geometry, Proc. IEEE, 80 (1992), 1412--1434.

....tree, hull tree, quad tree, R tree, grid file, metablock tree. 3 Further Information Many textbooks and monographs have been written on data structures, e.g. 1, 3, 5, 6, 7, 8, 9, 10, 13, 14, 16, 17, 15, 19] Recent papers surveying the state of the art in data structures include [2, 4, 12, 18]. The LEDA project [11] aims at developing a C library of efficient and reliable implementations of sophisticated data structures. 4 ....

Y.-J. Chiang and R. Tamassia. Dynamic algorithms in computational geometry. Proc. IEEE, 80(9):1412--1434, Sept. 1992.

No context found.

Y. Chiang and R. Tamassia, "Dynamic Algorithms in Computational Geometry," Brown University Deptartment of Computer Science technical report CS-91-24, 1991.

No context found.

Y. Chiang and R. Tamassia. Dynamic algorithms in computational geometry. Tech Report CS--91--24, Department of Computer Science, Brown University, 1991.

No context found.

Yi-Jen Chiang and Roberto Tamassia. Dynamic algorithms in computational geometry. Technical Report CS-91-24, Department of Computer Science, Brown University, March 1991.

No context found.

Y-J. Chiang and R. Tamassia. Dynamic algorithms in computational geometry. Proceedings of IEEE, Special Issue on Computational Geometry, 80(9):362-381, 1992.

No context found.

Y.-J. Chiang and R. Tamassia. Dynamic algorithms in computational geometry. Proc. of the IEEE, 80:1412-1434, 1992.

No context found.

Y.-J. Chiang and R. Tamassia. Dynamic algorithms in computational geometry. Proc. IEEE, 80(9):1412--1434, Sept. 1992.

No context found.

Y. Chiang and R. Tamassia, \Dynamic Algorithms in Computational Geometry", Proc. of the IEEE, Special Issue on Computational Geometry, G. Toussaint (Ed.), 80(9), 1992.

No context found.

Y. Chiang and R. Tamassia, "Dynamic Algorithms in Computational Geometry", Proc. of the IEEE, Special Issue on Computational Geometry, G. Toussaint (Ed.), 80(9), 1992.

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