In this paper we have observed and shown that ternary systems are more promising than the more traditional binary systems used in computers. In particular, ternary number system, heaps on ternary trees, and quicksort with 3 partitions do indicate some theoretical advantages over the more established binary systems. The magic Napierian e plays the crucial role to establish the results. The experimental data, supporting the analysis, have also been presented. Keywords: Analysis of algorithms; Performance evaluation; Quicksort; Heaps; Divide and conquer technique 1 Introduction With the invention of computers, 2-parametric algebra, number system and graphs among other systems started to flourish with accelerated speed. Boolean algebra got its important applications in computer technology, binary number system has occupied the core of computer arithmetic, and binary trees have become inseparable in Revised version of ref. no. CAM 2974. y Corresponding Author. mathematical analysis...

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.

In this report a new data strucutre named M-heaps is proposed. This data structure is a modi cation of the well known binary heap data structure. The new structure supports insertion in constant time and deletion in O(log n) time. Finally a generalization of the data structure to d ary M-heaps is presented. This structure has similar time-bounds for insertion and deletion.

An elementary approach is given to studying the recurrence relations associated with generalized heaps (or d-heaps), cost of optimal merge, and generalized divide-and-conquer minimization problems. We derive exact formulae for the solutions of all such recurrences and give some applications. In particular, we present a precise probabilistic analysis of Floyd's algorithm for constructing d-heaps when the input is randomly given. A variant of d-heap having some interesting combinatorial properties is also introduced.