Abstract

Abstract. In this paper we present a new data structure for implementing heapsort algorithm for pairs of which can be simultaneously stored and processed in a single register. Since time complexity of Carlsson type variants of heapsort has already achieved a leading coefficient of 1, concretely nlg n + nlg lg n, and lower bound theory asserts that no comparison based in-place sorting algorithm can sort n data in less than ⌈lg(n!) ⌉ ≈ n lg n − 1.44n comparisons on the average, any improvement in the number of comparisons can only be achieved in lower terms. Our new data structure results in improvement in the linear term of the time complexity function irrespective of the variant of the heapsort algorithm used. This improvement is important in the context that some of the variants of heapsort algorithm, for example weak heapsort although not in-place, are near optimal and is away from the theoretical bound on number of comparisons by only 1.54n.

Citations