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

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Yongxi Cheng, Xiaoming Sun, Yiqun Lisa Yin
• Keywords: D-dimensional Array, Dimension, DM 2008, Real Number