M. Atallah and J.-J. Tsay. On the parallel decomposability of geometric problems. Algorithmica,8: 209--231, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... The examples mentioned in [14, Section 2] are: orthog3 onal line segment intersection reporting, the all nearest neighbors problem [21] the 3D maxima problem [17] computing the measure of a set of axis parallel rectangles [9] computing the visibility of a set of line segments from a point [4], batched orthogonal range queries, and reporting pairwise intersections of axis parallel rectangles. We investigate if the distribution sweeping approach can be adapted to the cache oblivious model, and answer this in the a#rmative by developing optimal cache oblivious algorithms for each of the ....

....the second coordinate of the last maximal point identified. The solution for the three dimensional maxima problem makes iterated use of the plane sweep part for the two dimensional maxima problem. First all points a sorted w.r.t. the third coordinate. A divide and conquer approach described in [4] is then applied on the third coordinate. The aim is to produce for each strip a stream of the points contained in the strip, with the points sorted w.r.t. decreasing first coordinate and with a point being marked if and only if it is a maximal point among the points in the strip. The base case ....

M. J. Atallah and J.-J. Tsay. On the parallel-decomposability of geometric problems. Algorithmica, 8:209--231, 1992.

....the interconnection topology and the memory hierarchy, thus attaining optimal performance. Previous Work. For some of the classical geometric problems mentioned above, parallel algorithms were preProceedings of the International Parallel and Distributed Processing Symposium (IPDPS02) sented in [2] which run on a particular parallel architecture consisting of a d dimensional array of p processors, each provided with constant storage, connected to a single conventional RAM. On such a machine, these algorithms run in O n log n (p log p) time, thus attaining a speedup of # over ....

.... (relatively to local memory accesses) and submachine locality (relatively inter processor communication) whereas only the former type of locality was considered in [9] Our strategy combines the standard distribution sweeping with an orthogonal partitioning method similar to the one adopted in [2, 6], organizing the computation and the data movements so to exploit the hierarchical nature of the local memories as well as the clustered structure of the machine. We show that when bandwidth and latency increase geometrically with the cluster size (this scenario captures a wide family of ....

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M. Atallah and J. Tsay. On parallel decomposability of geometric problems. Algorithmica, 8:209--231, 1992.

....development of parallel algorithms which exhibit maximum locality with respect to both, the interconnection topology and the memory hierarchy, thus attaining optimal performance. Previous Work. For some of the classical geometric problems mentioned above, parallel algorithms were pre sented in [2] which run on a particular parallel architecture consisting of a d dimensional array of p processors, each provided with constant storage, connected to a single conventional RAM. On such a machine, these algorithms run in O n log n= p 1 1=d log p) time, thus attaining a speedup of p 1 ....

.... (relatively to local memory accesses) and submachine locality (relatively inter processor communication) whereas only the former type of locality was considered in [9] Our strategy combines the standard distribution sweeping with an orthogonal partitioning method similar to the one adopted in [2, 6], organizing the computation and the data movements so to exploit the hierarchical nature of the local memories as well as the clustered structure of the machine. We show that when bandwidth and latency increase geometrically with the cluster size (this scenario captures a wide family of ....

[Article contains additional citation context not shown here]

M. Atallah and J. Tsay. On parallel decomposability of geometric problems. Algorithmica, 8:209--231, 1992.

....27] Several suggestions have been made regarding the simulation of parallel algorithms as EM algorithms. This includes the results of Chiang et al. 11] on simulating PRAM algorithms and the results of Dehne et al. 17] and Dittrich et al. [20] on simulating BSP, CGM and BSP algorithms (see also [8, 32]) 1.3 New Results Cormen and Goodrich [13] posed the challenge of combining BSP like parallel algorithms with the requirements for parallel disk I O. Solutions based on probabilistic methods were presented in [17] and [20] In this paper, we present deterministic solutions which are based on a ....

Atallah, M., and Tsay, J.-J. On the parallel decomposability of geometric problems. Algorithmica 8 (1992), 209--231.

....rounds, and O( n log n p ) local computation per round. Our algorithm is deterministic and is also more scalable than the algorithm given in [5] in that it is eOEcient and applicable for a larger range of values for the ratio n=p. Our approach (which is very dioeerent from the one presented in [2, 11]) presents two particular strengths. First, all inter processor communications are restricted to usages of a small set of simple communication operations. This has the eoeect of making the algorithms both easy to implement, in that all communications are performed by calls to a standard highly ....

M. Atallah and J. Tsay. On the parallel-decomposability of geometric problems. In Proceedings of the 5th Annual ACM Symposium on Computational Geometry, pages 104113, 1989.

....is also listed as a major goal in the recent Grand Challenges report [6] Yet, only little theoretical work has been done for designing scalable parallel algorithms for Computational Geometry. The first and, to our knowledge, only previous theoretical paper to address this problem was [1]. The model considered there was a host machine with O(n) memory attached to a systolic array of size p with O(1) memory per processors. This model suffers however from fact that data has to be frequently swapped between the host and the systolic array, and this I O bottleneck is the main factor ....

....optimal or at least efficient for a wide range of ratios n p 1 We present new techniques for designing efficient scalable parallel geometric algorithms, which are independent of the communication network. A particular strength of our approach, which is very different from the one presented in [1], is that all inter processor communication is restricted to a constant number of two types of global routing operations: global sort and segmented broadcast (to be explained in Section 2) In a nutshell, the basic idea for our methods is as follows: We try to combine 1 Note that, if there exists ....

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M. J. Atallah and J.-J. Tsay. On the parallel-decomposability of geometric problems. Proc. 5th Annu. ACM Sympos. Comput. Geom., pages 104--113, 1989.

....[DFM95] the upper envelope represents a very commonly used concept since it permits, for instance, to compute the visibility horizon from a given viewpoint. Recently, the development of parallel algorithms for solving geometric problems represents an important research issue (see, for example, [AT89, BSG90, TD92, DFRC93]) Indeed, a lot of data are usually available as inputs to geometric algorithms and a suitable and efficient parallel solution seems to be very useful. To this aim, we have studied and implemented a parallel algorithm for computing the upper envelope of segments, which parallelizes the optimal ....

M. Atallah and J. Tsay. On the parallel decomposability of geometric problems. Proceedings 5 th Annual ACM Symposium on Computational Geometry, pages 104--113, 1989.

....of ratios n p . The design of such scalable algorithms is also listed as a major goal in the recent Grand Challenges report [10] Yet, only little theoretical work has been done for designing scalable parallel algorithms for computational geometry problems. A related problem was studied in [2, 19]. The model considered there was a host machine with O(n) memory attached to a systolic array of size p with O(1) memory per processors. This model suffers however from the fact that data has to be frequently swapped between the host and the systolic array, and this I O bottleneck is the main ....

....(e.g. for the mesh) We present new techniques for designing efficient scalable parallel geometric algorithms. Our results are independent of the communication network (e.g. mesh, hypercube, fat tree) A particular strength of our approach, which is very different from the one presented in [2, 9], is that all interprocessor communication is restricted to a constant number of usages of one single global routing operation: global sort. In a nutshell, the basic idea for our methods is as follows: We try to combine optimal sequential algorithms for a given problem with an efficient global ....

[Article contains additional citation context not shown here]

M. J. Atallah and J.-J. Tsay. On the parallel-decomposability of geometric problems. Proc. 5th Annu. ACM Symposium on Computational Geometry, pages 104--113, 1989.

....for these models are discussed in the full version of this paper. To a large extent they are based on modified versions of two of the main paradigms discussed above, namely distribution sweeping and batch filtering. We can also rely on the many way divide and conquer approach of Atallah and Tsay [5], which can be extended to the I O model. To implement distribution sweeping in these models we take advantage of deterministic distribution tech niques recently developed by Nodine and Vitter [27] for optimal deterministic sorting. To implement batch filtering, we can use disk striping [28] ....

M. J. Atallah & J. -J. Tsay,, "On the Parallel- Decomposability of Geometric Problems,," Algorith- mica 8 (1992), 209 231.

....finds with the best solution from any higher level. As we scan, we maintain an active set A i for each strip fl i . A i is the set of points in fl i for which we do not yet have either a certificate or a definite answer as to the identity of FN b (p) The following lemma, due to Atallah and Tsay [5] bounds the size of A i . Lemma 2.1 [5] At all times during the sweep, jA i j 4 for all fl i . Although there can be no more than a constant number (4) of points in A i at a time, these are not required to be the last four points in fl i that the sweep line passed. Nevertheless, since there ....

....level. As we scan, we maintain an active set A i for each strip fl i . A i is the set of points in fl i for which we do not yet have either a certificate or a definite answer as to the identity of FN b (p) The following lemma, due to Atallah and Tsay [5] bounds the size of A i . Lemma 2. 1 [5]: At all times during the sweep, jA i j 4 for all fl i . Although there can be no more than a constant number (4) of points in A i at a time, these are not required to be the last four points in fl i that the sweep line passed. Nevertheless, since there are only a constant number, we can keep ....

[Article contains additional citation context not shown here]

M. J. Atallah and J. -J. Tsay,, "On the ParallelDecomposability of Geometric Problems," Algorithmica 8 (1992), 209--231.

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M. Atallah and J.-J. Tsay. On the parallel decomposability of geometric problems. Algorithmica,8: 209--231, 1992.

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M. Atallah and J.-J. Tsay. On the parallel decomposability of geometric problems. Algorithmica,8: 209--231, 1992.

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M. Atallah and J.-J. Tsay. On the parallel decomposability of geometric problems. Algorithmica,8: 209--231, 1992.

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M. Atallah and J.-J. Tsay. On the parallel decomposability of geometric problems. Algorithmica, 8:209-- 231, 1992.

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M. Atallah and J.-J. Tsay. On the parallel decomposability of geometric problems. Algorithmica,8: 209--231, 1992.

No context found.

M. J. Atallah and J.-J. Tsay. On the parallel-decomposability of geometric problems. Algorithmica, 8:209--231, 1992.

No context found.

M. J. Atallah and J.-J. Tsay. On the parallel-decomposability of geometric problems. Proc. 5th Annu. ACM Symposium on Computational Geometry, pp. 104113, 1989.

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