In this work a new algorithm for quaternion-based spatial rotation is presented which reduces the number of underlying real multiplications. The performing of a quaternion-based rotation using a rotation matrix takes ...
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In this work a new algorithm for quaternion-based spatial rotation is presented which reduces the number of underlying real multiplications. The performing of a quaternion-based rotation using a rotation matrix takes 15 ordinary multiplications, 6 trivial multiplications by 2 (left-shifts), 21 additions, and 4 squarings of real numbers, while the proposed algorithm can compute the same result in only 14 real multiplications (or multipliers-in a hardware implementation case), 43 additions, 4 right-shifts (multiplications by 1/4), and 3 left-shifts (multiplications by 2).
We consider the special case of the two functions coarsest partitioning problem, where one of the functions is a cyclic permutation and the other arbitrary. Here we present a parallel algorithm on a CRCW PRAM that sol...
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We consider the special case of the two functions coarsest partitioning problem, where one of the functions is a cyclic permutation and the other arbitrary. Here we present a parallel algorithm on a CRCW PRAM that solves the above partitioning problem inO(α(n)log(β(n)))time usingO(n)processors, wherenis the set cardinality,β(n)is the number of distinct prime factors ofn,andα(n)is the sum of the exponents of the primes in the factorization *** almost all cases the algorithm runs inO(loglognlogloglogn)time withnprocessors.
This note points out and corrects an error in the algorithm proposed in [Ting-Yem Ho, Yue-Li Wang and Ming-Tsan Juan, A linear time algorithm for finding all hinge vertices of a permutation graph, Information Processi...
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This note points out and corrects an error in the algorithm proposed in [Ting-Yem Ho, Yue-Li Wang and Ming-Tsan Juan, A linear time algorithm for finding all hinge vertices of a permutation graph, Information Processing Letters 59 (2) (1996) 103–107].
There exist a variety of algorithms for the convex hull problem in the plane. The input to all of these is the set of points in terms of their coordinates. In this short note, a convex hull algorithm is presented in w...
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ISBN:
(纸本)9780897915069
There exist a variety of algorithms for the convex hull problem in the plane. The input to all of these is the set of points in terms of their coordinates. In this short note, a convex hull algorithm is presented in which the points are specified not through their coordinates but in terms of the distances between pairs of them in the form of a distance matrix. Some applications where this is the case are mentioned, and the algorithm's performance is analyzed and shown to be O(n2) in the worst case.
Let A, B, and C be three n×n matrices. We investigate the problem of verifying whether AB=C over the ring of integers and finding the correct product AB. Given that C is different from AB by at most k entries, we...
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