Andrei-Horia Mogos

Three Variants of the Master Theorem

The theory of algorithms complexity is of great importance in both theoretical and applied computer science. One of its main topics is the study of the recurrence relations as a way of representing algorithms complexities. In this paper we propose three variants of the Master Theorem, easier to apply than the standard variant. We also provide proofs for the proposed results and a comparative discussion.

A New Asymptotic Notation: Weak Theta

Algorithms represent one of the fundamental issues in computer science, while asymptotic notations are widely accepted as the main tool for estimating the complexity of algorithms. Over the years a certain number of asymptotic notations have been proposed. Each of these notations is based on the comparison of various complexity functions with a given complexity function. In this paper, we define a new asymptotic notation, called “Weak Theta,” that uses the comparison of various complexity functions with two given complexity functions. Weak Theta notation is especially useful in characterizing complexity functions whose behaviour is hard to be approximated using a single complexity function. In addition, in order to highlight the main particularities of Weak Theta, we propose and prove several theoretical results: properties of Weak Theta, criteria for comparing two complexity functions, and properties of a new set of complexity functions (also defined in the paper) based on Weak Theta. Furthermore, to illustrate the usefulness of our notation, we discuss an application of Weak Theta in artificial intelligence.

A Kernel Based Clustering Algorithm using Particle Swarm Optimization

Abstract Unsupervised learning is one of the major research areas in machine learning, while kernel methods provide eficient solutions for various statistical learning problems. In this paper we propose a kernel based clustering algorithm that uses the Particle Swarm Optimization technique and discriminant functions. The method represents a general framework for solving the clustering problem: once an appropriate clustering validation index is chosen for a given class of datasets, the method performs very well in solving the problem. The method automatically detects the clusters in a given dataset and also, automatically estimates the number of clusters. Due to the use of kernel functions, our approach can be used for both linearly separable and linearly non-separable clusters. Since our algorithm uses the Particle Swarm Optimization technique, parallel computation may be used, if necessary. We evaluate our method on various datasets and we discuss its capabilities.

TN4PM: A Textual Notation for Process Modelling

In this paper we compare three visual notations for modelling processes, and we propose a textual notation for modelling these processes. Our textual notation can be used just as a modelling notation, but it can also be used to translate the process models from one visual notation to another.

A Voting Approach for Comparing Several Swarm Intelligence Algorithms

In the last decades, social choice theory has gained a significant popularity. Its main application areas are social sciences, political sciences, economic sciences and computer science. Computational social choice is a new research area situated at the intersection of social choice theory and computer science. Another popular and relatively new research area is swarm intelligence that aims to propose and use bio-inspired algorithms for solving optimization problems. In this paper we propose a methodology of comparing various swarm intelligence algorithms using voting methods (an important topic in social choice theory). Also, as a case study, we use our methodology to compare three swarm intelligence algorithms (Particle Swarm Optimization, Cat Swarm Optimization, and Artificial Bee Colony) on several minimization functions. For the interpretation of our comparison results, we use two important theorems: No Free Lunch Theorem (from optimization theory) and Arrows Impossibility Theorem (from voting theory).

An Economy Model Based on Barter Exchanges between Software Agents

The interactions between parties within large, open systems are driven by trust. In this paper, we propose a model for barter exchanges based on reputation and trust values, which considers mechanisms for computing an agent’s trust according to a set of norms enforced by a central authority. Based on this model, the paper shows how self-interested agents manage to establish cooperation relationships in order to accomplishing their goals, being aware that the costs of future transactions depend on one’s reputation.