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Searching monotone multi-dimensional arrays

13 years 3 months ago
Searching monotone multi-dimensional arrays
A d-dimensional array of real numbers is called monotone increasing if its entries are increasing along each dimension. Given An,d, a monotone increasing d-dimensional array with n entries along each dimension, and a real number x, we want to decide whether x An,d, by performing a sequence of comparisons between x and some entries of An,d. We want to minimize the number of comparisons used. In this paper we investigate this search problem, we generalize Linial and Saks' search algorithm [2] for monotone 3-dimensional arrays to d-dimensions for d 4. For d = 4, our new algorithm is optimal up to the lower order terms. Key words: search algorithm, complexity, partially ordered set, monotone multi-dimensional array
Yongxi Cheng, Xiaoming Sun, Yiqun Lisa Yin
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where DM
Authors Yongxi Cheng, Xiaoming Sun, Yiqun Lisa Yin
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