Searching, Sorting and Randomised Algorithms for Central Elements and Ideal Counting in Posets
نویسندگان
چکیده
By the Central Element Theorem of Linial and Saks, it follows that for the problem of (generalised) sea.rching in posets, the information-theoretic lower bound of log N comparisons (where N is the number of order-ideals in the poset) is tight asymptotically. We observe that this implies that the problem of (generalised) sorting in posets has complexity 9( n . log N) (where n is the number of dements in the poset). We present schemes for (efficiently) transforming a randomised generation procedure for central dements (which often exists for some classes ofposets) into randomised proceduresfor approximatdy coUDting ideals in the poset and for testing if an a.rbitrary element is central.
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