Facultatea de Matematică şi Informatică / Faculty of Methematics and Informatics
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Item THE CONVEXITY IN THE COMPLEX OF MULTI-ARY RELATIONS(Romanian Society of Applied & Industrial Mathematics Universitatea din Pitesti, 2015) Braguţă, Galina; Cataranciuc, SergiuFor a complex of multi-ary relations [12] it is defined the concept of (k,m)-chain which is a generalization of the concept of chain known from the graph theory. Using (k,m)- chains it is introduced the concept of the distance function and it is proved that this function generate a convexity in the complex of multi-ary relations. It is operating with the concepts of convexity and convex hull, axiomatically defined by F.Levi [29] and we describe the iterative procedure to construct a convex hull for a subset of elements from the complex of multi-ary relations. [ABSTRACT FROM AUTHOR]Item ON NONTRIVIAL COVERS AND PARTITIONS OF GRAPHS BY CONVEX SETS(Institutul de Matematică şi Informatică al Academiei de Ştiinţe a Moldovei, 2018) Buzatu, Radu; Cataranciuc, SergiuIn this paper we prove that it is NP-complete to decide whet- her a graph can be partitioned into nontrivial convex sets. We show that it can be verified in polynomial time whether a graph can be covered by nontrivial convex sets. Also, we propose a re- cursive formula that establishes the maximum nontrivial convex cover number of a tree.Item dm-CONVEX FUNCTIONS IN THE COMPLEX OF MULTI-ARY RELATIONS(2017) Cataranciuc, Sergiu; Braguța, GalinaIn the present work the notions of dm-convexity and dm convex function are defined. Some properties of these functions are mentioned. We study the complexes of multi-ary relations for which the median function is dm-convex.Item EULER CHARACTERISTIC OF ABSTRACT CUBES COMPLEX(Valines SRL, 2014) Cataranciuc, SergiuFormula for the Euler characteristics for the In complex is deduced. The formula is expressed by cardinals of the groups of the homologies and by a number of m-dimensional abstract cubes from In.Item DERIVATION OF BOOLEAN FUNCTIONS BY THE BLOCKS METHOD(Valines SRL, 2014) Bulat, Mihai; Cataranciuc, Sergiu; Ciobanu, Iacob; Izbas, Vladimir; Zgureanu, AureliuA method for calculating using blocks of the partial derivatives of the boolean function which are represented in algebraic form { a polynomial form, disjunctive normal form and conjunctive normal form is proposed. The method can be used success- fully for functions which depend on a large number of variables (tens and hundreds). This method can be applied to solve many problems from di®erent areas such as: elaborating of encryption system with variable keys, some problems from discrete mathematics (systems isomorphism problem, problem of determining of chromatic number in graphs ect.).Item LOCATION PROBLEMS ON d - CONVEX SIMPLE PLANAR GRAPHS(CEP USM, 2015) Cataranciuc, Sergiu; Macoveiciuc, EliseiThe article examines the center and median problems on graphs with special structure. In scientific works these are frequently called location problems on graphs. Although efficient solutions for graphs with some well-known properties have been found, in general case the problem remains complex. In this paper the structure of median and center in a d-convex simple planargraph Gis studied.We evaluate the connection between median/center of a graph Gwith mentioned properties and median/center of a tree, determined by G.Item COERENŢA ELEMENTELOR ÎNTR-UN COMPLEX DE RELAŢII MULTI-ARE(CEP USM, 2015) Cataranciuc, SergiuÎn articol este generalizată noţiunea de coerenţă simplă a elementelor unui complex de relaţii multi-are. Interpretând elementele complexului de relaţii ca simplexe abstracte, sunt introduse noţiunile de t-coerenţă şi (t q) coerenţă. Sunt demonstrate rezultate ce ţin de relaţia de coerenţă generalizată a simplexelor abstracte.Item SEARCH TREE-BASED APPROACH FOR THE P-MEDIAN PROBLEM USING THE ANT COLONY OPTIMIZATION ALGORITHM(Academy of Sciences of Moldova, 2014) Bodnariuc, Gabriel; Cataranciuc, SergiuIn this paper we present an approximation algorithm for the p-median problem that uses the principles of ant colony optimization technique. We introduce a search tree that keeps the partial solutions during the solution process of the p-median problem. An adaptation is proposed that allows ant colony optimization algorithm to perform on this tree and obtain good results in short time.Item CLASE DE SUBGRAFURI STABILE ÎN ORIENTAREA TRANZITIVĂ A GRAFURILOR(CEP USM, 2015) Cataranciuc, Sergiu; Grigoriu, NicolaeÎn articol sunt analizate clasele de subgrafuri stabile, folosite la caracterizarea grafurilor tranzitiv orientabile și la studierea proprietăţilor acestora. Subgrafurile stabile reprezintă un suport în construirea orientării tranzitive a unui graf, precum şi pentru determinarea numărului acestora. De asemenea, sunt prezentate condiţiile necesare şi suficiente pentru ca un graf să fie tranzitiv orientabil.Item CONVEX GRAPH COVERS(Academy of Sciences of Moldova, 2015) Buzatu, Radu; Cataranciuc, SergiuWe study some properties of minimum convex covers and minimum convex partitions of simple graphs. We establish existence of graphs with fixed number of minimum convex covers and minimum convex partitions. It is known that convex p-cover problem is NP-complete for p\geq3 [5]. We prove that this problem is NP-complete in the case p=2. Also, we study covers and partitions of graphs when respective sets are nontrivial convex.