Dimensionality reduction aims at providing low-dimensional representations of high-dimensional data sets. Many new nonlinear methods have been proposed for the last years, yet the question of their assessment and comparison remains open. This paper first reviews some of the existing quality measures that are based on distance ranking and K-ary neighborhoods. Next, the definition of the corankin...

Our weighted-tree similarity algorithm matches buyers and sellers in e-Business environments. We use arc-labeled, arc-weighted trees to represent the products (or services) sought/offered by buyers/sellers. Partial product descriptions can be represented via subtrees missing in either or both of the trees. In order to take into account the effect of a missing subtree on the similarity between t...

Given a simple graph G = (V,E), a subset S of the vertices is called a global defensive alliance if S is a dominating set and for every vertex v in S at least half of the vertices in the closed neighborhood of v are in S. Similarly, a subset S is called a global offensive alliance if S is a dominating set and for every vertex v not in S at least half of the vertices in the closed neighborhood o...

which reduce to (n + 1) for a = b = c = 1. We refine Cayley’s formula by showing that Pn(a, b, c) counts rooted forests by the number of trees and the number of proper vertices, which are vertices that are less than all of their proper descendants. Moreover, other evaluations of Pn(a, b, c) have similar interpretations for other types of trees and forests: k-ary trees, forests of ordered trees,...

Gossiping is the process of information diiusion in which each node of a network holds a packet that must be communicated to all other nodes in the network. We consider the problem of gossiping in communication networks under the restriction that communicating nodes can exchange up to a xed number p of packets at each round. In the rst part of the paper we study the extremal case p = 1 and we e...

This study considers the addition of relation to an organization structure such that the communication of information between every member in the organization becomes the most efficient. This paper proposes a model of adding relation to a linking pin organization structure where every pair of siblings in a complete K-ary tree of height H is adjacent. When a new edge between the root and a node ...

It is known that task scheduling problem of an intree with unit time tasks and unit time communication delays onto a limited number of processors is NP-hard. In this paper, we show that such a problem is approximable within a factor of 3 if we assume a complete k-ary intree with at most (k − 1) constant communication delay. Also we prove that the problem is approximable within a factor of 2 if ...

I-language over simple type structure is considered. Type Y== (0 --t (0 -+ 0)) + (0 -+ 0) is called a binary tree type because of the isomorphism between binary trees and closed terms of this type. Therefore any closed term of type Y+(Y-P ... -P (Y + Y) ) represents an n-ary tree function. The problem is to characterize tree operations represented by the closed terms of the examined type. It is...

Genetic algorithms (GAs) are probabilistic search algorithms that are loosely based on biological evolution. Analyzing genetic algorithms has proven di cult, for a variety of reasons, but a landscape paradigm that rigorously models the search of GAs has become increasingly popular in their analysis. So far much of this analysis concerns binary representations, where each member of the populatio...

The category of group-graded modules over an abelian group G is a monoidal category. For any bicharacter of G this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have n-ary multiplications between various graded components. They possess universal enveloping algeb...