Related papers: Analysis of Sorting Algorithms by Kolmogorov Compl…

We study the computational complexity of some explainable clustering problems in the framework proposed by [Dasgupta et al., ICML 2020], where explainability is achieved via axis-aligned decision trees. We consider the $k$-means,…

The analyses of many algorithms and data structures (such as digital search trees) for searching and sorting are based on the representation of the keys involved as bit strings and so count the number of bit comparisons. On the other hand,…

Algorithms that exploit sort orders are widely used to implement joins, grouping, duplicate elimination and other set operations. Query optimizers traditionally deal with sort orders by using the notion of interesting orders. The number of…

Kolmogorov complexity of a finite binary word reflects both algorithmic structure and the empirical distribution of symbols appearing in the word. Words with symbol frequencies far from one half have smaller combinatorial richness and…

Link prediction in graphs is an important task in the fields of network science and machine learning. We investigate a flexible means of regularization for link prediction based on an approximation of the Kolmogorov complexity of graphs…

We study in which way Kolmogorov complexity and instance complexity affect properties of r.e. sets. We show that the well-known 2log n upper bound on the Kolmogorov complexity of initial segments of r.e.\ sets is optimal and characterize…

We study the computably enumerable sets in terms of the: (a) Kolmogorov complexity of their initial segments; (b) Kolmogorov complexity of finite programs when they are used as oracles. We present an extended discussion of the existing…

Kolmogorov complexity theory is used to tell what the algorithmic informational content of a string is. It is defined as the length of the shortest program that describes the string. We present a programming language that can be used to…

Much of the copious literature on the subject of sorting has concentrated on minimizing the number of comparisons and/or exchanges/copies. However, a more appropriate yardstick for the performance of sorting algorithms is based on the total…

Motivated by recent best case analyses for some sorting algorithms and based on the type of complexity we partition the algorithms into two classes: homogeneous and non homogeneous algorithms. Although both classes contain algorithms with…

In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides…

This work studies rearrangement problems involving the sorting of robots or objects in stack-like containers, which can be accessed only from one side. Two scenarios are considered: one where every robot or object needs to reach a…

In this paper we are proposing a new sorting algorithm, List Sort algorithm, is based on the dynamic memory allocation. In this research study we have also shown the comparison of various efficient sorting techniques with List sort. Due the…

The halting problem is undecidable --- but can it be solved for "most" inputs? This natural question was considered in a number of papers, in different settings. We revisit their results and show that most of them can be easily proven in a…

We introduce algorithmic information theory, also known as the theory of Kolmogorov complexity. We explain the main concepts of this quantitative approach to defining `information'. We discuss the extent to which Kolmogorov's and Shannon's…

The two most prominent solutions for the sorting problem are Quicksort and Mergesort. While Quicksort is very fast on average, Mergesort additionally gives worst-case guarantees, but needs extra space for a linear number of elements.…

Optimal shelflisting invites profit maximization to become sensitive to the ways in which purchasing decisions are order-dependent. We study the computational complexity of the corresponding product arrangement problem when consumers are…

Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and computational complexity theory -- in the discrete setting of bits and Turing machines. Over real numbers, on the other hand, the…

We have proposed novel measures based on the Kolmogorov complexity for use in complex system behavior studies and time series analysis. We have considered background of the Kolmogorov complexity and also we have discussed meaning of the…

It is well known that normality can be described as incompressibility via finite automata. Still the statement and the proof of this result as given by Becher and Heiber (2013) in terms of "lossless finite-state compressors" do not follow…