The Information-Theoretic Bound is Good for Merging

Let A=(al > > a,) and B=(bl > > b,) be given ordered lists: also let there be given some order relations between ai's and bj's. Suppose that an unknown total order exists on A tAB which is consistent with all these relations (= a linear extension of the partial order) and we wish to find out this total order by comparing pairs of elements at:bs. If the partial order has N linear extensions, then the Information Theoretic Bound says that log2 N steps will be required in the worst case from any such algorithm. In this paper we show that there exists an algorithm which will take no more than C log2 N comparisons where C (log2 ((x/+ 1)/2))-1. The computation required to determine the pair at:bs to be compared has length polynomial in (m + n). The constant C is best possible. Many related results are reviewed.