Multi-dimensional Arrays with Levels

Tiling Multi-dimensional Arrays

Searching monotone multi-dimensional arrays

In this paper we investigate the problem of searching monotone multi-dimensional arrays. We generalize Linial and Saks’ search algorithm [2] for monotone 3-dimensional arrays to d-dimensions with d ≥ 4. Our new search algorithm is asymptotically optimal for d = 4.

Probabilistic Models for Incomplete Multi-dimensional Arrays

In multiway data, each sample is measured by multiple sets of correlated attributes. We develop a probabilistic framework for modeling structural dependency from partially observed multi-dimensional array data, known as pTucker. Latent components associated with individual array dimensions are jointly retrieved while the core tensor is integrated out. The resulting algorithm is capable of handl...

Einstein summation for multi-dimensional arrays

One of the most common data abstractions, at least in scientific computing, is the multi-dimensional array. A numerical algorithm may sometimes conveniently be expressed as a generalized matrix multiplication, which computes a multi-dimensional array from two other multi-dimensional arrays. By adopting index notation with the Einstein summation convention, an elegant tool for expressing general...

Searching On Multi-Dimensional Arrays with Partial Order

In this paper we investigate the problem of searching on d-dimensional arrays with partial order. We generalize Linial and Saks’ search algorithm [2] for 3 dimension to arbitrary dimension d. Our new algorithms require at most d d−1 n + O(n) comparisons. It is optimal for d = 4.