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.

[1]  Michael E. Saks,et al.  Every Poset Has a Central Element , 1985, J. Comb. Theory, Ser. A.

[2]  Michael E. Saks,et al.  Searching Ordered Structures , 1985, J. Algorithms.