B. Chazelle. Filtering search: A new approach to query-answering. SIAM Journal on Computing, 15:3:703--724, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....n) nodes of T that v j updates. We further process each node in T so that it contains a list of cover two life ranges. This is a list of intervals consisting of the pairwise intersections of the life spans in the node. For example, assume that a node s contains the life spans [1, 7] 3, 4] and [5, 6]. The list of cover two at s is [3, 4] and [5, 6] If a vertical segment is to be deleted from s at instances x 1 , x 2 or x 7 , then s will be exposed after the deletion. But if the deletion occurs at instance x 3 , x 4 , x 5 or x 6 then, since the cover of s is 2 at this instance, s will not be ....

....each node in T so that it contains a list of cover two life ranges. This is a list of intervals consisting of the pairwise intersections of the life spans in the node. For example, assume that a node s contains the life spans [1, 7] 3, 4] and [5, 6] The list of cover two at s is [3, 4] and [5, 6]. If a vertical segment is to be deleted from s at instances x 1 , x 2 or x 7 , then s will be exposed after the deletion. But if the deletion occurs at instance x 3 , x 4 , x 5 or x 6 then, since the cover of s is 2 at this instance, s will not be exposed by deleting v j . Our parallel algorithm ....

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B. Chazelle, "Filtering search: A new approach to query-answering", SIAM J. Comput., 15(1986), pp. 703--724.

....hierarchy. 1.2 Previous Results Range searching has been studied extensively in the RAM model. In the planar case, for example, some of the best known structures answer queries in O(log N T log (2N T ) time using linear space and in O(log N T ) time using N) space, respectively [18, 19]. Refer to a recent survey for further results [3] In the I O model, the B tree [21, 9] supports one dimensional range queries in O(log B N T B) memory transfers using linear space. In two dimensions, one has to use #(N log B log B N ) space to obtain an O(log B N T B) query bound [8, ....

B. Chazelle. Filtering search: a new approach to queryanswering. SIAM J. Comput., 15(3):703--724, 1986.

....in Section 2.1. In Section 2.1.2, we present some useful data structures and algorithms that are available in the literature. These data structures and algorithms are used as tools to obtain new results in the succeeding chapters. Among others, the filtering search technique of Chazelle [Cha86] plays an important role and will be presented here in a more comprehensive yet concise way, compared to the original. It should be noted that one drawback of this technique is that it cannot be adapted for counting problems and its dynamization seems rather difficult to achieve. Another basic ....

....intersecting q. In the interval stabbing problem the query q is a point and we have to report all the intervals in S that enclose this point (this problem is often called the one dimensional point enclosure problem) In the following we describe window list , a simple data structure of Chazelle [Cha86] for solving this problem. This window list will be used as a secondary structure of the ff slab tree for solving the two dimensional orthogonal range searching problem in Section 2.3.2. i 1 W W W 1 curProfile = minProfile = 2 Figure 2.1: Illustration of the construction of Window list ....

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B. Chazelle. Filtering search: a new approach to query-answering. SIAM J. Comput., 15:703--724, 1986.

.... inside the triangle t j (Figure 9) This type of query is common in computational geometry: for example, Chazelle gave an optimal O(log m r) algorithm for the related problem of finding the subset of m isothetic rectangles which contain a query point, where r is the number of rectangles returned [3]. x y Figure 9. Points and triangles within the same layer. This problem can be mapped onto another classical one through the following transformation: let u i (i = 1; 2; 3) denote the inward unit normals to the edges of the triangles. Given some choice of origin in the plane, we can associate ....

B.M. Chazelle. Filtering search: a new approach to query answering. In IEEE Symposium on Foundatons of Computer Science, pages 122--132, Tucson, AZ, November 1983.

....in high dimensional space. In range searching problems, there is a need to find points in a k dimensional space which intersect a given query window. Orthogonal query problems have been well investigated, and a number of good data structures, such as the range search tree have been proposed [185, 180, 21, 22]. In particular, the bucketing method [48] which is similar to a k d tree using arbitrary splitting planes has been proposed. Tokuyama [166] propose a theoretic method for orthogonal clipping with applications to nearest neighbour queries. A more general non orthogonal case has also been studied ....

B. Chazelle. Filtering search: A new approach to query-answering. SIAM Journal on Computing, 15:703--724, 1986.

....shortest distance (path) in interval [r; 2r] achieving O( log n) update time per edge deletion. The algorithm is adapted to maintain all pairs shortest distance (paths) in O( n) update time. For the case when query is to report the shortest path, we use the concept of ltering search [1] to reduce the update time further to O(min(n n) 3 Maintaining all pairs reachability and shortest paths in interval [d; 2d] In this section we design an ecient algorithms for maintaining all pairs reachability and shortest paths corresponding to paths of length in interval [d; 2d] A ....

....paths in nonsparse graphs. 6.1 Improved update time for path reporting query If the query is to report the shortest path between two vertices, we can achieve better update time for maintaining all pairs shortest paths than shown in the Theroem 6.1. We use the following idea of ltering search [1] : If output of a query is of size O(l) we can perform O(l) extra work to answer the query without a ecting the optimum query time of O(l) Recall the data structure L d used for maintaining all pairs reachability corresponding to paths of length 2 [d; n] in section 4. The data structure built ....

Bernard Chazelle. Filtering search : A new approach to query-answering. SIAM J. Comput., 15:(3),703-724, 1986.

....which points lie in the range, i.e. report the points P = P, Pd) such that A P g B,A2 P2 g Ba, and A Ps B. The range searchi g problem has many applications in such areas as database design snd computer graphics. The problem has been studied in gret detail. See for example [1,2,4,6,24,25]. In the case the structure is static, i.e. no points have to be inerted or deleted the best knowns result is by Chazelle[4] who constructs a structure that uses space O(nl. and has a query time of O(k log n) Many trade offs can be obtained between the query time and the amount of space ....

....searchi g problem has many applications in such areas as database design snd computer graphics. The problem has been studied in gret detail. See for example [1,2,4,6,24,25] In the case the structure is static, i.e. no points have to be inerted or deleted the best knowns result is by Chazelle[4] who constructs a structure that uses space O(nl. and has a query time of O(k log n) Many trade offs can be obtained between the query time and the amount of space required (see e.g. Scholten and Overmars[2) In this paper we study the rane searching problem on a 2 dimensional rid, i.e. ....

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Chazelle, B., Filtering search: A new approach to query-answering, Proc. th Annual Syrup. on Foundations of Comluter Science, 1983, 122-132. (to appear in SIAM J. Comp.)

....capability to dynamic data structures. Also, trade o#s between space and time are possible. Their techniques explore the theory of range trees. 2.1.5 Filtering search One of the most elegant techniques in range searching is that of filtering search. This technique was explored by Chazelle [Cha86] although it was implicitly used in a few previous results (e.g. McC85] The technique is only applicable in range reporting search, where the size of the result can grow as large as the original dataset. The basic principle of filtering search is quite simple; when the output of a query is ....

....applied this idea to di#erent domains. Ramaswamy [Ram97] combined this idea with B trees to support indexing 17 for constraint and temporal databases. Kriegel et al. KPS00] evaluate the implementation of this technique in the SQL procedural language of the Oracle8i server. Another result of [Cha86] was the first optimal data structure for twodimensional range search, on a pointer machine. Solutions based on the range tree would achieve optimal time, but with slightly suboptimal space O(n log n) Chazelle showed that it was a simple matter to apply the principle of filtering search, to ....

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B. Chazelle. Filtering search: a new approach to query answering. SIAM Journal of Computing, 15(3):703--724, 1986.

....redundancy O(1) such that every query of size T is covered with at most O(t 1) blocks. 2.2.2 Indexing schemes for 4 sided workloads We now describe an algorithm by which we can create an indexing scheme for any range query workload. Our structure is based upon Chazelle s filtering technique [5]. We assume without loss of generality that N = ae k B, for some integers ae 2 and k 1. We first partition our data set of N points into L 0 = N=aeB sets S 0;j , for 1 j L 0 , based upon their x order. Each set S 0;j contains aeB points and fits into ae blocks. We say that the sets form ....

B. Chazelle. Filtering search: a new approach to queryanswering. SIAM J. Comput., 15:703--724, 1986.

....sex, weight, salary etc. A typical orthogonal range query is of the form find all males of age between 30 and 40 years with an income between 20,000 and 40,000 . The orthogonal range searching problem has numerous applications and has been studied extensively for the last decades, see e.g. [1, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 16, 17, 20, 22, 24, 25, 26, 27, 30, 31, 40, 41, 42, 43, 45, 46, 47]. Willard [43] gives a comprehensive list of references on the subject and gives applications to the theory of databases. For surveys see, e.g. the survey by Agarwal [1] and the books by Mehlhorn [27] and Preparate and Shamos [31] In this paper we consider various orthogonal range searching ....

....# b 1 , a d # v d # b d . For three dimensions we obtain the following result. Theorem 1 For the static three dimensional range reporting problem in R 3 there exists a data structure supporting queries in time O(log n k) and requiring space O(n log 1 # n) Chazelle in 1986 [13] gave a data structure for three dimensions with query time O(log 2 n k) and using space O(nlog 2 n log log n) Willard in 1992 [42] improved the query time of Chazelle by a factor O(log log n) using fusion trees. Overmars in 1988 [30] gave a data structure with query time O(log n log log n ....

[Article contains additional citation context not shown here]

B. Chazelle. Filtering search: a new approach to query-answering. SIAM Journal on Computing, 15(3):703--724, 1986.

....of the problem on O(B 2 ) points. The structure was necessary since to pay for a visit to a child node v i , we needed to find Theta(B) points in the slab corresponding to v i satisfying the query. The idea of charging some of the query cost to the output size is often called filtering [51], and the idea of using a static structure on O(B 2 ) elements in each node has been called the bootstrapping paradigm [151, 152] Finally, the ideas of weight balancing and global rebuilding were used to obtain worst case efficient update bounds. All these ideas have been used in the ....

....to the ones used by van Kreveld and Overmars in divided k d trees [146] In Section 5.2 below we discuss the cross tree further. 5. 1 Logarithmic query structure The O(log B N T=B) query data structure is based on ideas from the corresponding internal memory data structure due to Chazelle [51]. The structure consists of a fan out log B N base tree over the x coordinates of the N points. As previously an x range is associated with each node v and it is subdivided into log B N slabs by v s children v 1 ; v 2 ; v log B N . We store all the points in the x range of v in four ....

B. Chazelle. Filtering search: a new approach to query-answering. SIAM J. Comput., 15(3):703--724, 1986.

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B. Chazelle. Filtering search: A new approach to query-answering. SIAM Journal on Computing, 15:3:703--724, 1986.

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B. Chazelle, Filtering search A new approach to query answering, SIAM J. Comput. 15 (1986), pp. 703-724.

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Bernard Chazelle. Filtering search: A new approach to query-answering. SIAM J. Computing, 15(3):703-724, 1986.

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B. Chazelle, 1986, "Filtering search: A new approach to query-answering", SIAM J. Comput, 15(3), pp. 703--724.

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B. Chazelle. Filtering search: a new approach to query-answering. SIAM J. Comput., 15:703--724, 1986.

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Bernard Chazelle. Filtering search: A new approach to query-answering. SIAM J. Computing, 15(3):703-724, August 1986.

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B. Chazelle, 1986, "Filtering search: A new approach to query-answering", SIAM J. Comput, 15(3), pp. 703--724.

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B. Chazelle, Filtering Search: A new approach to query-answering, SIAM J. Comput. , 15, 3, 1986, pp.703--724.

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B. Chazelle. Filtering Search: A new approach to query-answering, SIAM J. Comput., 15, 3, pp.703-724, 1986.

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B. Chazelle, "Filtering Search: A New Approach To Query-Answering", SIAM J. COMPUT., Vol. 15, No. 3, August 1986.

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B. Chazelle, Filtering Search: A New Approach to Query-Answering, SIAM J. Comput., 15, 3, 1986, pp.703-724.

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B. Chazelle. Filtering search: A new approach to query-answering. SIAM Journal on Computing, 15:3:703--724, 1986.

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B. Chazelle, Filtering search: A new approach to query-answering, SIAM J. Comput., 15:3 (1986), pp. 703-724.

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B. Chazelle. Filtering Search: A new approach to queryanswering SIAM Journal on Computing, 15:703--724, 1986.

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