Peter Su. Efficient parallel algorithms for closest point problems. PhD thesis, Dartmouth College, 1994. PCS-TR94-238. 152  Home/Search   Document Details and Download   Summary   Related Articles   Check

....jch microsoft.com. 4 CADSI, 3150 Almaden Expwy Suite 104, San Jose, CA 95118, USA. dafna cadsi.com. Received June 1, 1997; revised March 10, 1998. Communicated by F. Dehne. 244 G. E. Blelloch, J. C. Hardwick, G. L. Miller, and D. Talmor mostly specialized for uniform distributions [8] [11]. One reason is that the dynamic nature of the problem can result in significant interprocessor communication. This is particularly problematic for nonuniform distributions. A second problem is that the parallel algorithms are typically much more complex than their sequential counterparts. This ....

....with high probability. The work of the algorithm is concentrated in the divide phase, and merging simply glues the solutions together. Since a point can appear in more than one subproblem, trimming techniques are used to avoid blow up. A simplified version of this algorithm was considered by Su [11]. He showed that whereas sampling does indeed evenly divide the problem, the expansion factor is close to 6 on all the distributions he considered. This will lead to an algorithm that is at best one sixth work efficient, and therefore, pending further improvements, is not a likely candidate for ....

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P. Su. Efficient Parallel Algorithms for Closest Point Problems. Ph.D. thesis, PCS-TR94-238, Department of Computer Science, Dartmouth College, Hanover, NH, 1994. Design and Implementation of a Practical Parallel Delaunay Algorithm 269

....As far as we can determine the main importance of the uniform Poisson distribution for DT is that the distribution is easy to generate and thus useful for running experiments. One drawback is that many implemented parallel algorithms are tuned to work most efficiently for the uniform distributions [37, 35] but fail to be efficient for nonuniform distributions. Here we define new point distributions for which we can find efficient parallel algorithms and which include all the distributions from the applications above. For these distributions we must prove new structure theorems. Our distributions ....

P. Su. Efficient parallel algorithms for closest point problems. Technical Report PCS-TR94-238, Dartmouth College, NH, 1994. PhD Thesis.

....algorithms, which have the advantage of generalizing to arbitrary dimensionality, and will be discussed in some depth here. In two dimensions, there are faster algorithms based upon divide andconquer and sweepline techniques, which will be discussed here only briefly. Refer to Su and Drysdale [68, 67] for an overview of these and other two dimensional Delaunay triangulation algorithms. Incremental insertion algorithms operate by maintaining a Delaunay triangulation, into which vertices are inserted one at a time. The earliest such algorithm, introduced by Lawson [43] is based upon edge ....

Peter Su. Efficient Parallel Algorithms for Closest Point Problems. Ph.D. thesis, Dartmouth College, Hanover, New Hampshire, May 1994.

....example, serializing the merge step of a divide and conquer algorithm, as in [38] reduces this communication, but introduces a serial bottleneck that severely limits scalability in terms of both parallel speedup and achievable problem size. The use of decomposition techniques such as bucketing [28, 11, 37, 35], or striping [14] can also reduce communication, but relies on the input dataset having a uniform spatial distribution of points in order to avoid load imbalances between processors. Unfortunately, while most real world problems are not this uniform, few authors report the performance of their ....

....achieve only a small fraction of the perfect speedup over good serial code running on one processor. Again, direct comparison is difficult because few authors quote speedups over good serial code. Of those that do, the 2D algorithm by Su achieved speedup factors of 3.5 5. 5 on a 32 processor KSR 1 [35], for a parallel efficiency of 11 17 , while the 3D algorithm [28] by Merriam achieved speedup factors of 6 20 on a 128 processor Intel Gamma, for a parallel efficiency of 5 16 . Both of these results were for uniform datasets. The 2D algorithm by Chew et al. [10] which solves the more general ....

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Peter Su. Efficient parallel algorithms for closest point problems. PhD thesis, Dartmouth College, 1994. PCSTR94 -238.

....example, serializing the merge step of a divide and conquer algorithm, as in [38] reduces this communication, but introduces a serial bottleneck that severely limits scalability in terms of both parallel speedup and achievable problem size. The use of decomposition techniques such as bucketing [28, 11, 37, 35], or striping [14] can also reduce communication, but relies on the input dataset having a uniform spatial distribution of points in order to avoid load imbalances between processors. Unfortunately, while most real world problems are not this uniform, few authors report the performance of their ....

....achieve only a small fraction of the perfect speedup over good serial code running on one processor. Again, direct comparison is difficult because few authors quote speedups over good serial code. Of those that do, the 2D algorithm by Su achieved speedup factors of 3.5 5. 5 on a 32 processor KSR 1 [35], for a parallel efficiency of 11 17 , while the 3D algorithm [28] by Merriam achieved speedup factors of 6 20 on a 128 processor Intel Gamma, for a parallel efficiency of 5 16 . Both of these results were for uniform datasets. The 2D algorithm by Chew et al. [10] which solves the more general ....

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Peter Su. Efficient parallel algorithms for closest point problems. PhD thesis, Dartmouth College, 1994. PCS-TR94-238.

....algorithms. The development of parallel algorithms is not as advanced. As a first step researchers have developed many theoretical parallel algorithms [7, 1, 8, 26, 20, 12] However, there have been very few efficient implementations, and these few depend on having a uniform distribution of points [16, 24, 22]. Attempts to implement the theoretically good algorithms have met with limited success [22] There are several obstacles to constructing good practical parallel Delaunay triangulation algorithms: 1) the known parallel solutions are highly irregular and dynamic, 2) they require significant ....

.... developed many theoretical parallel algorithms [7, 1, 8, 26, 20, 12] However, there have been very few efficient implementations, and these few depend on having a uniform distribution of points [16, 24, 22] Attempts to implement the theoretically good algorithms have met with limited success [22]. There are several obstacles to constructing good practical parallel Delaunay triangulation algorithms: 1) the known parallel solutions are highly irregular and dynamic, 2) they require significant inter processor communication, and (3) they have very large constants in their asymptotical work ....

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Peter Su. Efficient parallel algorithms for closest point problems. PhD thesis, Dartmouth College, 1994. PCS-TR94-238.

....analysis of how often implementations of these algorithms perform each operation. The rest of this section briefly describes the various algorithmic approaches. More detailed descriptions of the algorithms, including pseudocode, can be found in Chapter 2 of the first author s Ph.D. thesis [24]. This study was supported in part by the funds of the National Science Foundation, DDM 9015851, and by a Fulbright Foundation fellowship. 1 1.1. Divide and Conquer Guibas and Stolfi [17] gave an O(n log n) Delaunay triangulation algorithm that is asymptotically optimal in the worst case. The ....

Peter Su. Efficient parallel algorithms for closest point problems. Technical report, Dartmouth College, Nov. 1994.

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Peter Su. Efficient parallel algorithms for closest point problems. PhD thesis, Dartmouth College, 1994. PCS-TR94-238. 152

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