Related papers: Complexity of some algorithmic problems in groups:…
We discuss the frequent pattern mining problem in a general setting. From an analysis of abstract representations, summarization and frequent pattern mining, we arrive at a generalization of the problem. Then, we show how the problem can be…
Garside calculus is the common mechanism that underlies a certain type of normal form for the elements of a monoid, a group, or a category. Originating from Garside's approach to Artin's braid groups, it has been extended to more and more…
We consider the parameterised complexity of several list problems on graphs, with parameter treewidth or pathwidth. In particular, we show that List Edge Chromatic Number and List Total Chromatic Number are fixed parameter tractable,…
This article is a short introduction to generic case complexity, which is a recently developed way of measuring the difficulty of a computational problem while ignoring atypical behavior on a small set of inputs. Generic case complexity…
We study the interrelation of space functions of groups and the space complexity of the algorithmic word problem in groups.
Ensembles of artificial neural networks show improved generalization capabilities that outperform those of single networks. However, for aggregation to be effective, the individual networks must be as accurate and diverse as possible. An…
Consider the following generalization of the classic binary search problem: A searcher is required to find a hidden target vertex $x$ in a graph $G$. To do so, they iteratively perform queries to an oracle, each about a chosen vertex $v$.…
This paper contains a survey of recent developments in investigation of word equations in simple matrix groups and polynomial equations in simple (associative and Lie) matrix algebras along with some new results on the image of word maps on…
In this paper we study complexity of randomly generated instances of Dehn search problems in finitely presented groups. We use Crump-Mode-Jagers processes to show that most of the random instances are easy. Our analysis shows that for any…
Randomized search heuristics such as evolutionary algorithms, simulated annealing, and ant colony optimization are a broadly used class of general-purpose algorithms. Analyzing them via classical methods of theoretical computer science is a…
We revisit the selection problem, namely that of computing the $i$th order statistic of $n$ given elements, in particular the classic deterministic algorithm by grouping and partition due to Blum, Floyd, Pratt, Rivest, and Tarjan (1973).…
Recent works examine the relationship between the communication structure and the performance of a group in a problem solving task. Some conclude that inefficient communication networks with long paths outperform efficient networks on the…
This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly…
We generalize the classical knapsack and subset sum problems to arbitrary groups and study the computational complexity of these new problems. We show that these problems, as well as the bounded submonoid membership problem, are P-time…
We introduce the task of out-of-order membership to a formal language L, where the letters of a word w are revealed one by one in an adversarial order. The length |w| is known in advance, but the content of w is streamed as pairs (i, w[i]),…
A finitary automaton group is a group generated by an invertible, deterministic finite-state letter-to-letter transducer whose only cycles are self-loops at an identity state. We show that, for this presentation of finite groups, the…
We design new deterministic and randomized algorithms for computational problems in free solvable groups. In particular, we prove that the word problem and the power problem can be solved in quasi-linear time and the conjugacy problem can…
We suggest a new algorithm for finding a canonical representative of a given braid, and also for the harder problem of finding a $\sigma_1$-consistent representative. We conjecture that the algorithm is quadratic-time. We present numerical…
Ranking problems, also known as preference learning problems, define a widely spread class of statistical learning problems with many applications, including fraud detection, document ranking, medicine, credit risk screening, image ranking…
In this paper we explore fundamental concepts in computational complexity theory and the boundaries of algorithmic decidability. We examine the relationship between complexity classes \textbf{P} and \textbf{NP}, where $L \in \textbf{P}$…