Sumit Kumar Jha

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We revisit the method of Kirschenhofer, Prodinger and Tichy to calculate the moments of number of comparisons used by the randomized quick sort algorithm. We reemphasize that this approach helps in calculating these quantities with less computation. We also point out that as observed by Knuth this method also gives moments for total path length of a binary(More)
Three techniques for constructing reduced order models are presented and compared. The techniques are based on: 1) Model Reduction Using the Routh Stability Criterion by V. Krishnamurthy and V. Seshadri, 2) Higher Order Reduction by Coefficient Comparison by T. Manigandan and N. Devarajan 3) Clustering method for reducing order of linear system using Pade(More)
(Here and everywhere else in the paper, the expectation E[·] is with respect to the uniform probability distribution on {−1, 1}.) The Parseval’s identity is the fact that ∑ S⊆[n] f̂(S) 2 = E[f(x)]. In particular, if f is boolean-valued then this implies that ∑ S⊆[n] f̂(S) 2 = 1. Given f : {−1, 1} → R and i ∈ [n], we define the discrete derivative ∂if : {−1,(More)
The in-situ permutation algorithm due to MacLeod replaces (x1, · · · , xn) by (xp(1), · · · , xp(n)) where π = (p(1), · · · , p(n)) is a permutation of {1, 2, · · · , n} using at most O(1) space. Kirshenhofer, Prodinger and Tichy have shown that the major cost incurred in the algorithm satisfies a recurrence similar to sequence of the number of key(More)
We establish asymptotic expansions for factorial moments of following distributions: number of cycles in a random permutation, number of inversions in a random permutation, and number of comparisons used by the randomized quick sort algorithm. To achieve this we use singularity analysis of certain type of generating functions due to Flajolet and Odlyzko.
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