Data Flow Analysis and the Linear Programming Model

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.beThe general discussion of the data flow algorithmic models, and the linear programming problem with the variating by data flow criterion function coefficients are presented. The general problem is widely known in different names - data streams, incremental and online algorithms, etc. The more studied algorithmic models include mathematical statistics and clustering, histograms and wavelets, sorting, set cover, and others. Linear programming model is an addition to this list. Large theoretical knowledge exists in this as the simplex algorithm and as interior point methods but the flow analysis requires another interpretation of optimal plans and plan transition with variate coefficients. An approximate model is devised which predicts the boundary stability point for the current optimal plan. This is valuable preparatory information of applications, moreover when a parallel computational facility is supposed

Differential Balanced Trees and (0,1) Matrices

* The research was supported by INTAS 00-397 and 00-626 Projects.Links and similarities between the combinatorial optimization problems and the hierarchical search algorithms are discussed. One is the combinatorial greedy algorithm of step-by-step construction of the column-constraint (0,1) matrices with the different rows. The second is the base search construction of databases, - the class of the well known weight-balanced binary trees. Noted, that in some approximation each of the above problems might be interpreted in terms of the second problem. The constraints in matrices imply the novel concept of a differential balance in hierarchical trees. The obtained results extend the knowledge for balanced trees and prove that the known greedy algorithm for matrices is applicable in the world of balanced trees providing optimization on trees in layers

Chain Split and Computations in Practical Rule Mining

A novel association rule mining algorithm is composed, using the unit cube chain decomposition structures introduced in [HAN, 1966; TON, 1976]. [HAN, 1966] established the chain split theory. [TON, 1976] invented an excellent chain computation framework which brings chain split into the practical domain. We integrate these technologies around the rule mining procedures. Effectiveness is related to the intention of low complexity of rules mined. Complexity of the procedure composed is complementary to the known Apriori algorithm which is defacto standard in rule mining area

Lagrangean Approximation for Combinatorial Inverse Problems

Various combinatorial problems are effectively modelled in terms of (0,1) matrices. Origins are coming from n-cube geometry, hypergraph theory, inverse tomography problems, or directly from different models of application problems. Basically these problems are NP-complete. The paper considers a set of such problems and introduces approximation algorithms for their solutions applying Lagragean relaxation and related set of techniques

On Structural Resource of Monotone Recognition

Algorithmic resources are considered for elaboration and identification of monotone functions and some alternate structures are brought, which are more explicit in sense of structure and quantities and which can serve as elements of practical identification algorithms. General monotone recognition is considered on multi- dimensional grid structure. Particular reconstructing problem is reduced to the monotone recognition through the multi-dimensional grid partitioning into the set of binary cubes

Logic Based Pattern Recognition - Ontology Content (2)

Logic based Pattern Recognition extends the well known similarity models, where the distance measure is the base instrument for recognition. Initial part (1) of current publication in iTECH-06 reduces the logic based recognition models to the reduced disjunctive normal forms of partially defined Boolean functions. This step appears as a way to alternative pattern recognition instruments through combining metric and logic hypotheses and features, leading to studies of logic forms, hypotheses, hierarchies of hypotheses and effective algorithmic solutions. Current part (2) provides probabilistic conclusions on effective recognition by logic means in a model environment of binary attributes

Generating More Boundary Elements of Subset Projections

Composition problem is considered for partition constrained vertex subsets of n dimensional unit cube E^n . Generating numerical characteristics of E^n subsets partitions is considered by means of the same characteristics in 1 − n dimensional unit cube, and construction of corresponding subsets is given for a special particular case. Using pairs of lower layer characteristic vectors for E^(1-n) more characteristic vectors for E^n are composed which are boundary from one side, and which take part in practical recognition of validness of a given candidate vector of partitions

Logic Based Pattern Recognition - Ontology Content (1)

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.bePattern recognition (classification) algorithmic models and related structures were considered and discussed since 70s: – one, which is formally related to the similarity treatment and so - to the discrete isoperimetric property, and the second, - logic based and introduced in terms of Reduced Disjunctive Normal Forms of Boolean Functions. A series of properties of structures appearing in Logical Models are listed and interpreted. This brings new knowledge on formalisms and ontology when a logic based hypothesis is the model base for Pattern Recognition (classification)

The Boundary Descriptors of the n-dimensional Unit Cube Subset Partitioning

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.beThe specific class of all monotone Boolean functions with characteristic vectors of partitioning of sets of all true-vertices to be minimal is investigated. These characteristic vectors correspond to the column-sum vectors of special (0,1)-matrices – constructed by the interval bisection method