Searching On Multi-Dimensional Arrays with Partial Order
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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.