Optimal convex hull algorithms on enhanced meshes

Olariu, Stephan; Schwing, J.L.; Zhang, Jingyuan

doi:10.1007/bf01990523

Cited by 40 publications

(26 citation statements)

References 14 publications

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“…Recently, it has been shown that prefix sums can be computed efficiently on meshes with multiple broadcasting. More specifically, the following result has been proved in [23,32]. Merging two sorted sequences is one of the fundamental operations in computer science.…”

Section: Basicsmentioning

confidence: 93%

“…Recently, Olariu et al [32] have proposed a constant time algorithm to merge two sorted sequences of total length n stored in one row of a mesh with multiple broadcasting of size n ϫ n. More precisely, the following result was established in [32]. Since merging is an important ingredient in our ANN algorithm, we now give the details of the merging algorithm in [32]. To begin, using vertical buses, the first row is replicated in all rows of the mesh.…”

Section: Basicsmentioning

confidence: 98%

“…In turn, this processor has enough information to compute the position of a i in the sorted sequence. The simple merging algorithm that we just sketched is the main stepping stone in a time-optimal sorting algorithm developed in [32]. This algorithm implements the wellknown strategy of sorting by merging.…”

Section: Basicsmentioning

confidence: 98%

See 2 more Smart Citations

Time-Optimal Nearest-Neighbor Computations on Enhanced Meshes

Olariu

1996

Journal of Parallel and Distributed Computing

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Section: Basicsmentioning

confidence: 93%

Section: Basicsmentioning

confidence: 98%

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Time-Optimal Nearest-Neighbor Computations on Enhanced Meshes

Olariu

1996

Journal of Parallel and Distributed Computing

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“…1. We note that some reconfigurable mesh models proposed in the literature allow processors to fuse any number of their ports [3], [10], [12], [15], [18], [19]. In accord with other workers, we assume ideal bus communications [7], [10], [12], [13], [14].…”

Section: Introductionmentioning

confidence: 99%

Optimal algorithms for the multiple query problem on reconfigurable meshes, with applications

Bokka

Nakano

Olariu

et al. 2001

IEEE Trans. Parallel Distrib. Syst.

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AbstractÐThe main contribution of this work is to show that a number of fundamental and seemingly unrelated problems in database design, pattern recognition, robotics, computational geometry, and image processing can be solved simply and elegantly by stating them as instances of a unifying algorithmic framework that we call the Multiple Query problem. The Multiple Query problem (MQ, for short) is a 5-tuple ; e; h; ; È, where is a set of queries, e is a set of items, h is a set of solutions, : Â e 3 h is a function, and È is a commutative and associative binary operator over h. The input to the MQ problem consists of a sequence Q hq 1 ; q 2 ; . . . ; q m i of m queries from and of a sequence A ha 1 ; a 2 ; . . . a n i of n items from e. The goal is to compute, for every query q i (1 i m) its solution defined as q i ; A q i ; a 1 È q i ; a 2 È Á Á Á È q i ; a n . We begin by discussing a generic algorithm that solves a large class of MQ problems in O m p fn time on a reconfigurable mesh of size n p Â n p , where fn is the time necessary to compute the expression d 1 È d 2 È Á Á Á È d n with d i P h on such a platform. We then go on to show that the MQ framework affords us an optimal algorithm for the multiple point location problem on a reconfigurable mesh of size n p Â n p . Given a set A of n points and a set Q of m m n points in the plane, our algorithm reports, in O m p log log n time, all points of Q that lie inside the convex hull of A. Quite surprisingly, our algorithm solves the multiple point location problem without computing the convex hull of A which, in itself, takes n p time on a reconfigurable mesh of size n p Â n p . Finally, we prove an m p gn time lower bound for nontrivial MQ problems, where gn is the lower bound for evaluating the expression d 1 È d 2 È Á Á Á È d n with d i P h, on a reconfigurable mesh of size n p Â n p .

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“…A n umber of models have been proposed, and various techniques have been introduced to help develop constant running time algorithms for image processing, geometric and graph theoretic problems (refer to 7, 1, 3] for a survey of the various models and algorithms). Recent examples include constant time algorithms for sorting n numbers 4,8,5] and for determining the convex hull of n planar points 12,13].…”

Section: Introductionmentioning

confidence: 99%

Optimal Algorithms for Constrained Reconfigurable Meshes

Beresford‐Smith

Diessel

ElGindy

1996

Journal of Parallel and Distributed Computing

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This paper introduces a constrained recon gurable mesh model which incorporates practical assumptions about propagation delays on large sized buses. Simulations of AT 2 optimal recon gurable mesh algorithms on the constrained recon gurable mesh model are found to be non{optimal. Optimal solutions for the sorting and convex hull problems requiring less area are then presented. For the problems investigated, the constrained recon gurable mesh model predicts a continuum in performance between the recon gurable mesh and mesh of processors architectures.

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Optimal convex hull algorithms on enhanced meshes

Cited by 40 publications

References 14 publications

Time-Optimal Nearest-Neighbor Computations on Enhanced Meshes

Time-Optimal Nearest-Neighbor Computations on Enhanced Meshes

Optimal algorithms for the multiple query problem on reconfigurable meshes, with applications

Optimal Algorithms for Constrained Reconfigurable Meshes

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