Related papers: Analysis of Sorting Algorithms by Kolmogorov Compl…
We study the minimal complexity of tilings of a plane with a given tile set. We note that every tile set admits either no tiling or some tiling with O(n) Kolmogorov complexity of its n-by-n squares. We construct tile sets for which this…
When dealing with massive data sorting, we usually use Hadoop which is a framework that allows for the distributed processing of large data sets across clusters of computers using simple programming models. A common approach in implement of…
We determine the complexity of several constraint satisfaction problems using the heuristic algorithm, WalkSAT. At large sizes N, the complexity increases exponentially with N in all cases. Perhaps surprisingly, out of all the models…
The original Leapfrogging Samplesort operates on a sorted sample of size $s$ and an unsorted part of size $s+1$. We generalize this to a sorted sample of size $s$ and an unsorted part of size $(2^k-1)(s+1)$, where $k = O(1)$. We present a…
The ability to precisely quantify similarity between various entities has been a fundamental complication in various problem spaces specifically in the classification of cellular images. Contemporary similarity measures applied in the…
While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…
We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…
Modern comparison sorts like quicksort suffer from performance inconsistencies due to suboptimal pivot selection, leading to $(O(N^2))$ worst-case complexity, while in-place merge sort variants face challenges with data movement overhead.…
Sorting is the task of ordering $n$ elements using pairwise comparisons. It is well known that $m=\Theta(n\log n)$ comparisons are both necessary and sufficient when the outcomes of the comparisons are observed with no noise. In this paper,…
The paper questions the robustness of average case time complexity of the fast and popular quicksort algorithm. Among the six standard probability distributions examined in the paper, only continuous uniform, exponential and standard normal…
The last theme of Kolmogorov's mathematics research was algorithmic theory of information, now often called Kolmogorov complexity theory. There are only two main publications of Kolmogorov (1965 and 1968-1969) on this topic. So Kolmogorov's…
The clustering objects has become one of themes in many studies, and do not few researchers use the similarity to cluster the instances automatically. However, few research consider using Kommogorov Complexity to get information about…
Sundararajan and Chakraborty (2007) introduced a new version of Quick sort removing the interchanges. Khreisat (2007) found this algorithm to be competing well with some other versions of Quick sort. However, it uses an auxiliary array…
We present an extremely simple sorting algorithm. It may look like it is obviously wrong, but we prove that it is in fact correct. We compare it with other simple sorting algorithms, and analyse some of its curious properties.
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…
While modern general-purpose computing systems have ample amounts of memory, it is still the case that embedded computer systems, such as in a refrigerator, are memory limited; hence, such embedded systems motivate the need for strictly…
Algorithmic efficiency is essential to reducing energy and time usage for computational problems. Optimizing efficiency is important for tasks involving multiple resources, for example in stochastic calculations where the size of the random…
A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…
We present SPEC-RE, a new algorithm to sort complex eigenvalues, generated as the solutions to algebraic equations, whose coefficients are analytic functions of one or many, possibly complex parameters. The fact that the eigenvalues are…
We introduce a new sorting device for permutations which makes use of a pop stack augmented with a bypass operation. This results in a sorting machine, which is more powerful than the usual Popstacksort algorithm and seems to have never…