Related papers: Algorithmic Search in Group Theory

Quantum Search Algorithm made a big impact by being able to solve the search problem for a set with $N$ elements using only $O(\sqrt{N})$ steps. Unfortunately, it is impossible to reduce the order of the complexity of this problem, however,…

A quantum algorithm for combinatorial search is presented that provides a simple framework for utilizing search heuristics. The algorithm is evaluated in a new case that is an unstructured version of the graph coloring problem. It performs…

Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…

Tree search is a fundamental tool for planning, as many sequential decision-making problems can be framed as searching over tree-structured spaces. We propose an uncertainty-guided tree search algorithm for settings where the reward…

We develop a rounding method based on random walks in polytopes, which leads to improved approximation algorithms and integrality gaps for several assignment problems that arise in resource allocation and scheduling. In particular, it…

Grover's search algorithm is designed to be executed on a quantum mechanical computer. In this paper, the probabilistic wp-calculus is used to model and reason about Grover's algorithm. It is demonstrated that the calculus provides a…

First we consider pair-wise distances for literal objects consisting of finite binary files. These files are taken to contain all of their meaning, like genomes or books. The distances are based on compression of the objects concerned,…

The crucial but very confidential fact is brought into evidence that, as Kolmogorov himself repeatedly claimed, the mathematical theory of probabilities cannot be applied to physical, factual probabilistic situations because the factual…

Recommendation to groups of users is a challenging subfield of recommendation systems. Its key concept is how and where to make the aggregation of each set of user information into an individual entity, such as a ranked recommendation list,…

The multiple knapsack problem with grouped items aims to maximize rewards by assigning groups of items among multiple knapsacks, considering knapsack capacities. Either all items in a group are assigned or none at all. We propose algorithms…

Although heuristic search is one of the most successful approaches to classical planning, this planning paradigm does not apply straightforwardly to Generalized Planning (GP). This paper adapts the planning as heuristic search paradigm to…

Search-base algorithms have widespread applications in different scenarios. Grover's quantum search algorithms and its generalization, amplitude amplification, provide a quadratic speedup over classical search algorithms for unstructured…

The paper presents the main characteristics and a preliminary implementation of a novel computational framework named CompLog. Inspired by probabilistic programming systems like ProbLog, CompLog builds upon the inferential mechanisms…

Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin complexity of short strings. The…

A new quantum algorithm for a search problem and its computational complexity are discussed. It is shown in the search problem containing 2^n objects that our algorithm runs in polynomial time.

First the crucial but very confidential fact is brought into evidence that, as Kolmogorov himself repeatedly claimed, there exists no abstract theory of probabilities, simply because the factual concept of probability is itself unachieved:…

We study a novel problem of fairness in ranking aimed at minimizing the amount of individual unfairness introduced when enforcing group-fairness constraints. Our proposal is rooted in the distributional maxmin fairness theory, which uses…

This paper proposes an alternative language for expressing results of the algorithmic theory of randomness. The language is more precise in that it does not involve unspecified additive or multiplicative constants, making mathematical…

Understanding the similar properties of people involved in group search sessions has the potential to significantly improve collaborative search systems; such systems could be enhanced by information retrieval algorithms and user interface…

Social computation, whether in the form of searches performed by swarms of agents or collective predictions of markets, often supplies remarkably good solutions to complex problems. In many examples, individuals trying to solve a problem…