Searching monotone 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.

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.

Multi-Dimensional Heuristic Searching

A heuristic improvement technique referred to as multi-dimensional heuristics is presented. Instead of only applying the heuristic between two states X 1 and X 2 , when a distance esti­ mate of X 1 X 2 is needed, this technique uses a reference state R and applies the heuristic func­ tion to {X 1 ,R) and (X' 2 ,R) and compares the resulting values. If two states are close to each other, then th...

Tiling Multi-dimensional Arrays

A note on searching sorted unbalanced three-dimensional arrays

We examine the problem of searching sequentially for a desired real value (a key) within a sorted unbalanced three-dimensional finite real array. This classic problem can be viewed as determining the correct dimensional threshold function from a finite class of such functions within the array, based on sequential queries that take the form of point samples. This note addresses the challenge of ...