Related papers: The McDougal Cave and Counting issues
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations…
Given a network, the critical node detection problem finds a subset of nodes whose removal disrupts the network connectivity. Since many real-world systems are naturally modeled as graphs, assessing the vulnerability of the network is…
Clustering is an unsupervised technique of Data Mining. It means grouping similar objects together and separating the dissimilar ones. Each object in the data set is assigned a class label in the clustering process using a distance measure.…
Despite the increasing popularity of metaheuristics, many crucially important questions remain unanswered. There are two important issues: theoretical framework and the gap between theory and applications. At the moment, the practice of…
In this work, we study the generalized sorting problem, where we are given a set of $n$ elements to be sorted, but only a subset of all possible pairwise element comparisons is allowed. We look at the problem from the perspective of the…
The Algorithm Selection Problem is concerned with selecting the best algorithm to solve a given problem on a case-by-case basis. It has become especially relevant in the last decade, as researchers are increasingly investigating how to…
Many systems exhibit complex interactions between their components: some features or actions amplify each other's effects, others provide redundant information, and some contribute independently. We present a simple geometric method for…
In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.
We present a framework to analyze color documents of complex layout. In addition, no assumption is made on the layout. Our framework combines in a content-driven bottom-up approach two different sources of information: textual and spatial.…
Metaheuristic algorithms are becoming an important part of modern optimization. A wide range of metaheuristic algorithms have emerged over the last two decades, and many metaheuristics such as particle swarm optimization are becoming…
Online educational platforms organize academic questions based on a hierarchical learning taxonomy (subject-chapter-topic). Automatically tagging new questions with existing taxonomy will help organize these questions into different classes…
One of the fundamental problem in the theory of sorting is to find the pessimistic number of comparisons sufficient to sort a given number of elements. Currently 16 is the lowest number of elements for which we do not know the exact value.…
New sets (typically found by computer search) with Sidon constant equal to the square root of their cardinalities are given. For each integer $N$ there are only a finite number of groups of prime order containing $N$-element extreme sets.…
The first part of this article deals with theorems on uniqueness in law for \sigma-finite and constructive countable random sets, which in contrast to the usual assumptions may have points of accumulation. We discuss and compare two…
We investigate the special class of formulas made up of arbitrary but finite com- binations of addition, multiplication, and exponentiation gates. The inputs to these formulas are restricted to the integral unit 1. In connection with such…
In the past decade, Social Tagging Systems have attracted increasing attention from both physical and computer science communities. Besides the underlying structure and dynamics of tagging systems, many efforts have been addressed to unify…
Finding inclusion-minimal "hitting sets" for a given collection of sets is a fundamental combinatorial problem with applications in domains as diverse as Boolean algebra, computational biology, and data mining. Much of the algorithmic…
Algorithmic discrimination is an important aspect when data is used for predictive purposes. This paper analyzes the relationships between discrimination and classification, data set partitioning, and decision models, as well as…
The description of complex configuration is a difficult issue. We present a powerful technique for cluster identification and characterization. The scheme is designed to treat with and analyze the experimental and/or simulation data from…