Related papers: Yet Another Efficient Unification Algorithm
A classification algorithm, called the Linear Centralization Classifier (LCC), is introduced. The algorithm seeks to find a transformation that best maps instances from the feature space to a space where they concentrate towards the center…
Many learning algorithms are formulated in terms of finding model parameters which minimize a data-fitting loss function plus a regularizer. When the regularizer involves the l0 pseudo-norm, the resulting regularization path consists of a…
Clustering algorithms remain valuable tools for grouping and summarizing the most important aspects of data. Example areas where this is the case include image segmentation, dimension reduction, signals analysis, model order reduction,…
We introduce the open-ended, modular, self-improving Omega AI unification architecture which is a refinement of Solomonoff's Alpha architecture, as considered from first principles. The architecture embodies several crucial principles of…
In this paper, we intend to present a new algorithm to factorize large numbers. According to the algorithm proposed here, we prove that there is a common factor between p and q. With this procedure, the time of factorization considerably…
Optimization-based solvers play a central role in a wide range of signal processing and communication tasks. However, their applicability in latency-sensitive systems is limited by the sequential nature of iterative methods and the high…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
In multiobjective optimization, the result of an optimization algorithm is a set of efficient solutions from which the decision maker selects one. It is common that not all the efficient solutions can be computed in a short time and the…
Numerous sophisticated local algorithm were suggested in the literature for various fundamental problems. Notable examples are the MIS and $(\Delta+1)$-coloring algorithms by Barenboim and Elkin [6], by Kuhn [22], and by Panconesi and…
An algorithm $M$ is described that solves any well-defined problem $p$ as quickly as the fastest algorithm computing a solution to $p$, save for a factor of 5 and low-order additive terms. $M$ optimally distributes resources between the…
In this paper we relate a number of parsing algorithms which have been developed in very different areas of parsing theory, and which include deterministic algorithms, tabular algorithms, and a parallel algorithm. We show that these…
Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of…
Linear programming is the seminal optimization problem that has spawned and grown into today's rich and diverse optimization modeling and algorithmic landscape. This article provides an overview of the recent development of first-order…
We introduce a new and increasingly relevant setting for distributed optimization in machine learning, where the data defining the optimization are distributed (unevenly) over an extremely large number of \nodes, but the goal remains to…
We consider the distributed optimization problem for a multi-agent system. Here, multiple agents cooperatively optimize an objective by sharing information through a communication network and performing computations. In this tutorial, we…
Database query processing requires algorithms for duplicate removal, grouping, and aggregation. Three algorithms exist: in-stream aggregation is most efficient by far but requires sorted input; sort-based aggregation relies on external…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
Enumeration algorithms have been one of recent hot topics in theoretical computer science. Different from other problems, enumeration has many interesting aspects, such as the computation time can be shorter than the total output size, by…
Inspired by multigrid methods for linear systems of equations, multilevel optimization methods have been proposed to solve structured optimization problems. Multilevel methods make more assumptions regarding the structure of the…