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## Coarse-Grained Parallel Geometric Search (1999)

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### Other Repositories/Bibliography

Venue: | Journal of Parallel and Distributed Computing |

Citations: | 4 - 1 self |

### Citations

2032 |
Computational Geometry: An Introduction
- Preparata, Shamos
- 1985
(Show Context)
Citation Context ...of m query points q 1, ..., q m the line segment sji first intersected by the ray starting at qi in direction Dnext (m=O(n)); see Fig. 1. A sequential solution requires O(n log n) time and O(n) space =-=[19]-=-. 1 Research partially supported by the Natural Sciences and Engineering Research Council of Canada. 2 Corresponding author. 0743-7315 99 30.00 Copyright 1999 by Academic Press All rights of reproduct... |

1353 |
A bridging model for parallel computation
- VALIANT
- 1990
(Show Context)
Citation Context ...es PRAM algorithms optimally on distributed memory parallel systems. Valiant points out, however, that one may want to design algorithms that utilize local computations and minimize global operations =-=[21, 22]-=-. The BSP approach requires that g (=local computation speed router bandwidth) is low, or fixed, even for increasing number of processors. Gerbessiotis and Valiant [15] describe circumstances where PR... |

312 | Parallel merge sort
- Cole
- 1988
(Show Context)
Citation Context ...rs in the range 1, ..., N c for fixed constant c stored on a CGM, N p data items per processor, with respect to the CGM's processor numbering. The sort algorithm in [16] is based on Cole's merge sort =-=[6]-=-. The O((N p) log N ) local computation in [16] is due to a constant number of local sorts. Hence, by applying radix sort for the integer case, we obtain O(N p) localsCOARSE-GRAINED PARALLEL GEOMETRIC... |

214 |
General Purpose Parallel Architectures
- Valiant
- 1990
(Show Context)
Citation Context ...algorithms do not necessarily match the speedups observed on real machines [2, 20]. Given sufficient slackness in the 225s226 CHAN, DEHNE, AND RAU-CHAPLIN number of processors, Valiant's BSP approach =-=[22]-=- simulates PRAM algorithms optimally on distributed memory parallel systems. Valiant points out, however, that one may want to design algorithms that utilize local computations and minimize global ope... |

188 | at al. “A Comparison of Sorting Algorithms for the Connection
- Blelloch
- 1991
(Show Context)
Citation Context ...for all v # V0. without any catalogs but with (3) Processor Pi computes the catalogs of T0 with respect to Si only. We refer to this reduced version of T0 as T0, i. Note that |T0, i |=O((n p) log p). =-=(4)-=- Assume that all nodes of T0 have a unique index. Consider a line segment s in the catalog of the node v in T0 with index j(s). For each such line segment s, define a key *(s) obtained by concatenatin... |

174 | Direct bulk-synchronous parallel algorithms
- Gerbessiotis, Valiant
- 1992
(Show Context)
Citation Context ... minimize global operations [21, 22]. The BSP approach requires that g (=local computation speed router bandwidth) is low, or fixed, even for increasing number of processors. Gerbessiotis and Valiant =-=[15]-=- describe circumstances where PRAM simulations cannot be performed efficiently, among others if the factor g is high. Unfortunately, this is true for most currently available multiprocessors. The algo... |

137 |
Data Structures and Algorithms 3: Multi-dimensional Searching and Computational Geometry
- Mehlhorn
- 1984
(Show Context)
Citation Context ...alues with respect to some associative operator [8] (O((N p)) local computation). 3. SEGMENT TREE DEFINITION A well-known method for solving the next element search problem is to apply a segment tree =-=[3, 18, 19]-=-. Let s (x) i [q(x) i ] be the projection of the line segment si (query point qi, respectively) onto the x-axis, and let (x1, x2, ..., x2n) be the sorted sequence of the projections of the 2n endpoint... |

76 | Scalable parallel computational geometry for coarse grained multicomputers
- Dehne, Fabri, et al.
- 1993
(Show Context)
Citation Context ...e cost of a message also contains a constant overhead cost s. The value of s can be fairly large and the total message overhead cost can have a considerable impact on the speedup observed (see, e.g., =-=[8]-=-). We are therefore using a variation of the BSP model, referred to as coarse-grained multicomputer (CGM). A CGM is comprised of a set of p processors P 1, ..., P p with O(N p) local memory per proces... |

71 | Type Architecture, Shared Memory and the Corollary of Moest Potential - Snyder - 1986 |

50 | A randomized parallel 3D convex hull algorithm for coarse grained multicomputers
- Dehne, Deng, et al.
- 1995
(Show Context)
Citation Context ...that, this requires 2p virtual processors. Using integer sort, route n p queries to each processor such that a processor storing S(T i) receives n p queries whose search path contains the root of Ti. =-=(9)-=- Each processor processes the queries for its subtree Ti (1 plane sweep [19]. i p) by applying (10) Combine the results of Step 9 with those obtained in Step 6, using integer sort (by query ID). End o... |

43 |
Parallel computational geometry
- Akl, Lyons
- 1993
(Show Context)
Citation Context ...el algorithms; segment tree; simple polygon triangulation; trapezoidal map. 1. INTRODUCTION The next element search problem is a well-known problem in computational geometry and has many applications =-=[1]-=-. Given a set of n nonintersecting line segments s 1, ..., s n and a direction D next (without loss of generality we can assume that D next is the direction of the positive Y-axis), the next element s... |

40 |
An optimal worst case algorithm for reporting intersections of rectangles
- Bentley, Wood
- 1980
(Show Context)
Citation Context ...alues with respect to some associative operator [8] (O((N p)) local computation). 3. SEGMENT TREE DEFINITION A well-known method for solving the next element search problem is to apply a segment tree =-=[3, 18, 19]-=-. Let s (x) i [q(x) i ] be the projection of the line segment si (query point qi, respectively) onto the x-axis, and let (x1, x2, ..., x2n) be the sorted sequence of the projections of the 2n endpoint... |

40 | Parallel sorting by overpartitioning - Hui, Sevcik - 1994 |

30 | Scalable and Architecture Independent Parallel Geometric Algorithms with High Probability Optimal Time
- Dehne, Fabri, et al.
- 1994
(Show Context)
Citation Context ...g integer sort. (6) The queries are processed on the sublists to which they were sent in step 5, and the log p results for each query are collected in a single processor by using global integer sort. =-=(7)-=- Determine for each Ti the number, a(Ti ), of queries whose search path includes the root of Ti (1 i p). This can be computed by using global (8) integer sort and partial sum operations. Let b(Ti)=Wa(... |

24 | A comparison of shared and nonshared memory models of parallel computation
- ANDERSON, SNYDER
- 1991
(Show Context)
Citation Context ...per and outlines some important applications. 2. THE COARSE-GRAINED MULTICOMPUTER MODEL Speedup results for theoretical PRAM algorithms do not necessarily match the speedups observed on real machines =-=[2, 20]-=-. Given sufficient slackness in the 225s226 CHAN, DEHNE, AND RAU-CHAPLIN number of processors, Valiant's BSP approach [22] simulates PRAM algorithms optimally on distributed memory parallel systems. V... |

18 |
Parallel triangulation of a polygon in two calls to the trapezoidal map. Algorithmica
- Yap
- 1988
(Show Context)
Citation Context ...n the interior of a simple polygon into a set of triangles. 233s234 CHAN, DEHNE, AND RAU-CHAPLIN The above three problems can be reduced to O(1) next element search problems (obvious for 1 and 2; see =-=[23]-=- for 3). Hence, Theorem 1 applies to these problems as well and we obtain Corollary 1. The planar subdivision search problem, trapezoidal map problem, and triangulation problem for a simple polygon ca... |

15 | Scalable algorithms for bichromatic line segment intersection problems on coarse grained multicomputers
- Fabri, Devillers
- 1993
(Show Context)
Citation Context ...e next element search algorithm presented here implies immediate solutions for the point location, trapezoidal decomposition and triangulation problems. As in a previous paper by Develliers and Fabri =-=[13]-=-, our algorithm is based on a distributed implementation of segment trees which are of size O(n log n). This paper improves on [13] in several ways: v It studies the more general next element search p... |

14 |
Efficient Routing and Message Bounds for Optimal Paralle1 Algorithms
- Deng, Dymond
- 1995
(Show Context)
Citation Context ...bserved speedup, and it requires no assumption on g. Furthermore, it has been shown that minimizing the number of supersteps also leads to improved portability across different parallel architectures =-=[11, 21, 22]-=-. The above model has been used (explicitly or implicitly) in parallel algorithm design for various problems ([4, 7 10, 12, 14, 17]) and has shown very good practical timing results. We now list some ... |

13 | A note on coarse grained parallel integer sorting. Parallel Processing
- Chan, Dehne
- 1999
(Show Context)
Citation Context ...communication rounds. For practical implementations, a much simpler CGM integer sorting algorithm with 9 communication rounds, O(N p) memory per processor and O(N p) local computation can be found in =-=[5]-=-. v All-to-all broadcast. Every processor sends one message to all other processors [8]. This operation requires O((N p)) local computation. v Personalized all-to-all broadcast. Every processor (in pa... |

13 | Good programming style multiprocessors - Deng, Gu - 1994 |

13 |
Communication efficient parallel sorting
- Goodrich
- 1996
(Show Context)
Citation Context ...erations reduces to O(1) communication rounds for N p p: v Global sort. Sort O(N ) data items stored on a CGM, N p data items per processor, with respect to the CGM's processor numbering. As shown in =-=[16]-=-, for N p p it is possible to sort in O(1) communication rounds with O(N p) memory per processor and O((N p) log N ) local computation. v Global integer sort. Sort O(N ) integers in the range 1, ..., ... |

11 |
Aconvex hull algorithm on coarse grained multiprocessors
- Deng
- 1994
(Show Context)
Citation Context ... such that a processor storing S(T i) receives n p queries whose search path contains the root of Ti. (9) Each processor processes the queries for its subtree Ti (1 plane sweep [19]. i p) by applying =-=(10)-=- Combine the results of Step 9 with those obtained in Step 6, using integer sort (by query ID). End of algorithm. Theorem 2. Algorithm 2 solves the next element search problem for n line segments on a... |

6 | Scalable 2d convex hull and triangulation for coarse grained multicomputers - Ferreira, Rau-Chaplin, et al. - 1996 |

2 | Communication E#cient Parallel Sorting - Goodrich - 1996 |