Ovchinnikov

pp. 106-123

pp 288-304

 In this article the authors consider experimental evaluation of reducing computational complexity of algorithms of ultra-graph operations. According to the results of theoretical analysis of the algorithms of ultra-graph operations, procedures, which introduce the greatest contribution to their computational complexity, were defined; ways of its reducing were selected. With the help of special software contribution of optimizing transformations to reducing computational complexity of vertex addition was estimated. Experimental results showed high efficiency of the conversion process - total reduction of computational complexity of the algorithm was up to 87%.

The efficiency of using ordered set operations is considered by example of partitioning a complex system structure into subsystems. The article considers a formal definition of this problem as separation of the hypergraph vertex set into disjoint subsets. The article describes the main design routines of computer scheme partitioning by sequential algorithm. The partitioning process was fulfilled by using unordered and ordered set operations. The computation complexity assessment of both member functions was fulfilled. The efficiency of using ordered set operations may be proportional to the quantity of network elements.

In this paper, we present the two realizations networks partitioning: in set operations and with using hypergraph operations. The second variant partitioning description is more compact and clear. The asymptotic computation complexity of both realizations is equal. The formal description of multilevel hypergraph partitioning is received. This description make possible easily to estimate the transformations that demand very large quantity actions.

The decisive rules of algorithms execution ordered set operations are substantiated. Conditions for achieving maximum of multitude elements comparisons are formulated. The asymptotic computation complexities of operations are received. The efficiency of using ordered set operations is estimated.

Some operations reforming ultra- and hypergraphs are considered. These operations realize project procedures of analysis and synthesis the complex system structure using their mathematical models.

Some operations reforming ultra- and hypergraphs are considered. These operations realize project procedures of analysis and synthesis the complex system structure using their mathematical models

Some operations reforming ultra- and hypergraphs are considered. These operations realize project procedures of analysis and synthesis the complex system structure using their mathematical models.

In this paper, the unified concept of  ultra-, hyper- and usual directed and un directed graph is given. The connection between this types  of graph models is shown. The formal rules for  matrix and  analytical representations each type of graph are cited.