Abstract
This paper studies the average complexity on the number of comparisons for sorting algorithms. Its information-theoretic lower bound is nlgn−1.4427n+O(logn). For many efficient algorithms, the first nlgn term is easy to achieve and our focus is on the (negative) constant factor of the linear term. The current best value is −1.3999 for the MergeInsertion sort. Our new value is −1.4106, narrowing the gap by some 25%. An important building block of our algorithm is “two-element insertion,” which inserts two elements A and B, A<B, into a sorted sequence T. This insertion algorithm is still sufficiently simple for rigorous mathematical analysis and works well for a certain range of the length of T for which the simple binary insertion does not, thus allowing us to take a complementary approach together with the binary insertion.
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