Related papers: Complexity of some algorithmic problems in groups:…
The present paper gives a statistical adventure towards exploring the average case complexity behavior of computer algorithms. Rather than following the traditional count based analytical (pen and paper) approach, we instead talk in terms…
The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.
The subword complexity of a word $w$ over a finite alphabet $\mathcal{A}$ is a function that assigns for each positive integer $n$, the number of distinct subwords of length $n$ in $w$. The subword complexity of a word is a good measure of…
We study the problem of automatically computing the time complexity of concurrent object-oriented programs. To determine this complexity we use intermediate abstract descriptions that record relevant information for the time analysis (cost…
Grouping the nodes of a graph into clusters is a standard technique for studying networks. We study a problem where we are given a directed network and are asked to partition the graph into a sequence of coherent groups. We assume that…
Let $X$ be a finite set in $Z^d$. We consider the problem of optimizing linear function $f(x) = c^T x$ on $X$, where $c\in Z^d$ is an input vector. We call it a problem $X$. A problem $X$ is related with linear program $\max\limits_{x \in…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
Metaheuristics have gained great success in academia and practice because their search logic can be applied to any problem with available solution representation, solution quality evaluation, and certain notions of locality. Manually…
We initiate a systematic study of the time complexity of quantum divide and conquer algorithms for classical problems. We establish generic conditions under which search and minimization problems with classical divide and conquer algorithms…
Generalization in robotics is one of the most important problems. New generalization approaches use internet databases in order to solve new tasks. Modern search engines can return a large amount of information according to a query within…
Motivated by a historical combinatorial problem that resembles the well-known Josephus problem, we investigate circular partition algorithms and formulate problems in deterministic finite automata with practical algorithms. The historical…
We survey known results about the complexity of surjective homomorphism problems, studied in the context of related problems in the literature such as list homomorphism, retraction and compaction. In comparison with these problems,…
We build a general theory for characterizing the computational complexity of motion planning of robot(s) through a graph of "gadgets", where each gadget has its own state defining a set of allowed traversals which in turn modify the…
The scheduling problem is a key class of optimization problems and has various kinds of applications both in practical and theoretical scenarios. In the scheduling problem, probabilistic analysis is a basic tool for investigating…
Motivated by a theorem of Groves and Wilton, we propose the study of the lattice of numberings of isomorphism classes of marked groups as a rigorous and comprehensive framework to study global decision problems for finitely generated…
We study the densest subgraph problem and its NP-hard densest at-most-$k$ subgraph variant through the lens of learning-augmented algorithms. We show that, given a reasonably accurate predictor that estimates whether a node belongs to the…
We study two complexity notions of groups - a computable Scott sentence and the index set of a group. Finding the exact complexity of one of them usually involves finding the complexity of the other, but this is not the case sometimes. J.…
The problem addressed concerns the determination of the average number of successive attempts of guessing a word of a certain length consisting of letters with given probabilities of occurrence. Both first- and second-order approximations…
We give a ranker-based description using finite-index congruences for the variety $\boldsymbol{\mathrm{DAb}}$ of finite monoids whose regular $\mathcal{D}$-classes form Abelian groups. This combinatorial description yields a normal form for…
By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…