Soubhik Chakraborty

On why an algorithmic time complexity measure can be system invariant rather than system independent

The present paper argues that it suffices for an algorithmic time complexity measure to be system invariant rather than system independent (which means predicting from the desk).

A statistical analysis of an algorithm's complexity

Abstract In doing the statistical analysis of bubble sort program, we compute its execution times with various parameters. The statistical analysis endorses the specific quadratic pattern of the execution time on the number of items to be sorted. Next, a cursor along the future direction is indicated.

Software complexity : A statistical case study through insertion sort

The present paper makes use of factorial experiments to assess software complexity using insertion sort as an example. A new modeling for insertion sort is proposed. It might be of interest to implement the methodology in quicksort and other advanced algorithms.

Replacement sort revisited: The “gold standard” unearthed!

Abstract The present paper shows that for certain algorithms such as sorting, the parameters of the input distribution must also be taken into account, apart from the input size, for a more precise evaluation of computational and time complexity (average case only) of the algorithm in question (the so-called “gold standard”). Some concrete results are presented to warrant a new and improved model for replacement sort (also called selection sort) as T avg ( n , p 1 , p 2 , … p k ) = a 0 + b 0 n ( n - 1 ) / 2 + c 0 i ( n , p 1 , p 2 , … p k ) + ϵ , where the LHS gives the average case time complexity, n is the input size, p i ’s the parameters of the input distribution characterizing the sorting elements, i is the average number of interchanges which is a function of both the input size and the parameters, the rest of the terms arising due to linear regression and have usual meanings. The error term ϵ arises as we have fixed only the input size n in the model but varying the specific input elements and their relative positions in the array, for a particular distribution [H. Mahmoud, Sorting: A Distribution Theory, John Wiley and Sons, 2000]. The term n ( n - 1 ) / 2 represents the number of comparisons. We claim this to be an improvement over the conventional model, namely, T avg ( n ) = a + bn + cn 2 + ϵ , which stems from the O ( n 2 ) complexity for this algorithm. We argue that the new model in our opinion can be a guiding factor in distinguishing this algorithm from other sorting algorithms of similar order of average complexity such as bubble sort and insertion sort. Note carefully that the dependence of the number of interchanges on the parameters is more prominent for discrete distributions rather than continuous ones and we suspect this to be because the probability of a tie is zero in a continuous case. However, presence of ties and their relative positions in the array is crucial for discrete cases. And this is precisely where the parameters of the input distribution come into play. Those algorithms where ties have a greater influence on some of the computations will have greater influence of parameters of the input distribution in it. Another strength of the paper is that it brings up the close connection between algorithmic complexity and computer experiments , a crucial issue which is overlooked in the textbooks on algorithms . This is a paper on modeling rather than speed.

Partition Sort and Its Empirical Analysis

In the present paper we have introduced a new sorting algorithm named Partition Sort and performed its empirical study with necessary theoretical analysis. This algorithm was subjected to data coming from various standard probability distributions. Average Case analysis revealed that for some standard distributions it worked even more efficiently than the popular Hoare’s quicksort algorithm. The relative order of execution time, for different distributions, in descending order came out to be: Discrete Uniform < Binomial < Poisson < Standard Normal < Continuous Uniform.

A Novel Method of Hiding Message Using Musical Notes

Security has become an important topic for communication systems. It is a big challenge to provide secure communication in this unique network environment. We propose a novel approach to encrypt a message using musical notes and these musical notes have to be sent by the sender to the receiver. The receiver after receiving the musical notes decrypts it and gets back the original message.

How robust are average complexity measures? A statistical case study

Abstract In the present paper, the authors reject one of Knuth’s well known results on average case complexity in replacement (i.e. selection) sort and hence challenge the robustness of average complexity measures where the response variable is sensitive to ties.

Finite-difference time-domain method for modelling of seismic wave propagation in viscoelastic media

Abstract A finite difference formulation for the equations of SH waves in viscoelastic media has been developed and applied to the problem of an infinite half space with a buried source emitting a compressional pulse. A dispersion relation has been developed by employing the finite difference (FD) method, which has been used to discuss the stability criteria and also for obtaining the relation for phase and group velocities in viscoelastic media. Furthermore, the effect of variation of stability parameter on phase and group velocities; effect on the wave propagation with increase in dispersion parameter; and change in the wave propagation at different locations from the source have also been studied. The SH waves are found to be dispersive in viscoelastic media. The phase velocity increases with decrease in stability parameter. Furthermore, the location of the source has an important effect on the strength of the wave propagation in that the intensity of wave and therefore its longevity is inversely proportional to the distance from the source, implying that the wave will progressively die out exponentially.

Using Raga as a Cryptographic Tool

Music can be used as a special language of codes and ciphers. Music cipher is one possible way to communicate among many others. Musical notes with letters are equated in such a way as to make a work or phrase. Broadcast messages encrypted by the sender in the musical notes and decrypted by the receiver can help to protect the message from the intruder. The paper proposes raga as a cryptographic tool. Apart from the novelty, we discover some potential benefits.

A new sorting algorithm

We are introducing a new sorting algorithm.