scholarly journals Simulations between Network Topologies in Networks of Evolutionary Processors

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 183
Author(s):  
José Ángel Sánchez Martín ◽  
Victor Mitrana
Keyword(s):  
Complete Graph ◽  
Time Complexity ◽  
Star Graph ◽  
Constant Number ◽  
Grid Graph ◽  
Arbitrary Topology ◽  
Underlying Graph ◽  
Network Of Evolutionary Processors ◽  
Network Topologies ◽  
The Given

In this paper, we propose direct simulations between a given network of evolutionary processors with an arbitrary topology of the underlying graph and a network of evolutionary processors with underlying graphs—that is, a complete graph, a star graph and a grid graph, respectively. All of these simulations are time complexity preserving—namely, each computational step in the given network is simulated by a constant number of computational steps in the constructed network. These results might be used to efficiently convert a solution of a problem based on networks of evolutionary processors provided that the underlying graph of the solution is not desired.

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

Finding an Unknown Acyclic Orientation of a Given Graph

2009 ◽  
Vol 19 (1) ◽  
pp. 121-131 ◽  
Author(s):  
OLEG PIKHURKO
Keyword(s):  
Complete Graph ◽  
Discrete Mathematics ◽  
Np Hard ◽  
Worst Case ◽  
Acyclic Orientation ◽  
Multiplicative Factor ◽  
The Given

Let c(G) be the smallest number of edges we have to test in order to determine an unknown acyclic orientation of the given graph G in the worst case. For example, if G is the complete graph on n vertices, then c(G) is the smallest number of comparisons needed to sort n numbers.We prove that c(G) ≤ (1/4 + o(1))n2 for any graph G on n vertices, answering in the affirmative a question of Aigner, Triesch and Tuza [Discrete Mathematics144 (1995) 3–10]. Also, we show that, for every ϵ > 0, it is NP-hard to approximate the parameter c(G) within a multiplicative factor 74/73 − ϵ.

PLANE CURVES IN AN IMMERSED GRAPH IN ℝ2

2013 ◽  
Vol 22 (02) ◽  
pp. 1350003
Author(s):  
MARISA SAKAMOTO ◽  
KOUKI TANIYAMA
Keyword(s):  
Complete Graph ◽  
Closed Curve ◽  
Chord Diagram ◽  
Plane Curves ◽  
Generic Immersion ◽  
The Given

For any chord diagram on a circle there exists a complete graph on sufficiently many vertices such that any generic immersion of it to the plane contains a plane-closed curve whose chord diagram contains the given chord diagram as a sub-chord diagram. For any generic immersion of the complete graph on six vertices to the plane, the sum of averaged invariants of all Hamiltonian plane curves in it is congruent to one quarter modulo one-half.

scholarly journals ON THE EDGE OF DECIDABILITY IN COMPLEXITY ANALYSIS OF LOOP PROGRAMS

2012 ◽  
Vol 23 (07) ◽  
pp. 1451-1464 ◽  
Author(s):  
AMIR M. BEN-AMRAM ◽  
LARS KRISTIANSEN
Keyword(s):  
Second Language ◽  
Programming Language ◽  
Polynomial Time ◽  
Time Complexity ◽  
Complexity Analysis ◽  
Feasibility Problem ◽  
Polynomial Time Complexity ◽  
Turing Complete ◽  
The Given

We investigate the decidability of the feasibility problem for imperative programs with bounded loops. A program is called feasible if all values it computes are polynomially bounded in terms of the input. The feasibility problem is representative of a group of related properties, like that of polynomial time complexity. It is well known that such properties are undecidable for a Turing-complete programming language. They may be decidable, however, for languages that are not Turing-complete. But if these languages are expressive enough, they do pose a challenge for analysis. We are interested in tracing the edge of decidability for the feasibility problem and similar problems. In previous work, we proved that such problems are decidable for a language where loops are bounded but indefinite (that is, the loops may exit before completing the given iteration count). In this paper, we consider definite loops. A second language feature that we vary, is the kind of assignment statements. With ordinary assignment, we prove undecidability of a very tiny language fragment. We also prove undecidability with lossy assignment (that is, assignments where the modified variable may receive any value bounded by the given expression, even zero). But we prove decidability with max assignments (that is, assignments where the modified variable never decreases its value).

VORONOI DIAGRAMS FOR A TRANSPORTATION NETWORK ON THE EUCLIDEAN PLANE

2006 ◽  
Vol 16 (02n03) ◽  
pp. 117-144 ◽  
Author(s):  
SANG WON BAE ◽  
KYUNG-YONG CHWA
Keyword(s):  
Voronoi Diagram ◽  
Euclidean Plane ◽  
Transportation Network ◽  
Voronoi Diagrams ◽  
The Other ◽  
Constant Number ◽  
Time Path ◽  
The Given

This paper investigates geometric and algorithmic properties of the Voronoi diagram for a transportation network on the Euclidean plane. In the presence of a transportation network, the distance is measured as the length of the shortest (time) path. In doing so, we introduce a needle, a generalized Voronoi site. We present an O(nm2+ m3+ nm log n) algorithm to compute the Voronoi diagram for a transportation network on the Euclidean plane, where n is the number of given sites and m is the complexity of the given transportation network. Moreover, in the case that the roads in a transportation network have only a constant number of directions and speeds, we propose two algorithms; one needs O(nm + m2+ n log n) time with O(m(n + m)) space and the other O(nm log n + m2log m) time with O(n + m) space.

scholarly journals A Math Approach with Brief Cases towards Reducing Computational and Time Complexity in the Industrial Systems

2020 ◽  
Author(s):  
Yaroslav Matviychuk ◽  
Tomáš Peráček ◽  
Natalya Shakhovska
Keyword(s):  
Mathematical Models ◽  
Time Complexity ◽  
Order Reduction ◽  
Parametric Identification ◽  
Problem Area ◽  
Model Order ◽  
Industrial Systems ◽  
The Neural Network ◽  
Reduction Methods ◽  
The Given

The paper proposes a new principle of finding and removing elements of mathematical model, redundant in terms of parametric identification of the model. It allows reducing computational and time complexity of the applications built on the model. Especially this is important for AI based systems, systems based on IoT solutions, distributed systems etc. Besides, the complexity reduction allows increasing an accuracy of mathematical models implemented. Despite the model order reduction methods are well known, they are extremely depended however on the problem area. Thus, proposed reduction principles can be used in different areas, what is demonstrated in this paper. The proposed method for the reduction of mathematical models of dynamic systems allows also the assessment of the requirements for the parameters of the simulator elements to ensure the specified accuracy of dynamic similarity. Efficiency of the principle is shown on the ordinary differential equations and on the neural network model. The given examples demonstrate efficient normalizing properties of the reduction principle for the mathematical models in the form of neural networks.

scholarly journals The effect of network topology on optimal exploration strategies and the evolution of cooperation in a mobile population

2019 ◽  
Vol 475 (2230) ◽  
pp. 20190399 ◽  
Author(s):  
Igor V. Erovenko ◽  
Johann Bauer ◽  
Mark Broom ◽  
Karan Pattni ◽  
Jan Rychtář
Keyword(s):  
Network Topology ◽  
Complete Graph ◽  
Evolution Of Cooperation ◽  
Underlying Structure ◽  
Star Graph ◽  
Movement Model ◽  
Arbitrary Group ◽  
Public Goods Games ◽  
Current Location ◽  
Mobile Population

We model a mobile population interacting over an underlying spatial structure using a Markov movement model. Interactions take the form of public goods games, and can feature an arbitrary group size. Individuals choose strategically to remain at their current location or to move to a neighbouring location, depending upon their exploration strategy and the current composition of their group. This builds upon previous work where the underlying structure was a complete graph (i.e. there was effectively no structure). Here, we consider alternative network structures and a wider variety of, mainly larger, populations. Previously, we had found when cooperation could evolve, depending upon the values of a range of population parameters. In our current work, we see that the complete graph considered before promotes stability, with populations of cooperators or defectors being relatively hard to replace. By contrast, the star graph promotes instability, and often neither type of population can resist replacement. We discuss potential reasons for this in terms of network topology.

A Comparative Study of Different Techniques for Prime Testing in Implementation of RSA

2020 ◽  
Vol 1 (1) ◽  
pp. 1-7
Author(s):  
Kumarjit Banerjee ◽  
Satyendra Nath Mandal ◽  
Sanjoy Kumar Das
Keyword(s):  
Comparative Study ◽  
Prime Number ◽  
Time Complexity ◽  
Linear Equations ◽  
Prime Numbers ◽  
Security Level ◽  
Square Root ◽  
Rsa Cryptosystem ◽  
Rsa Algorithm ◽  
The Given

The RSA cryptosystem, invented by Ron Rivest, Adi Shamir and Len Adleman was first publicized in the August 1977 issue of Scientific American. The security level of this algorithm very much depends on two large prime numbers. The large primes have been taken by BigInteger in Java. An algorithm has been proposed to calculate the exact square root of the given number. Three methods have been used to check whether a given number is prime or not. In trial division approach, a number has to be divided from 2 to the half the square root of the number. The number will be not prime if it gives any factor in trial division. A prime number can be represented by 6n±1 but all numbers which are of the form 6n±1 may not be prime. A set of linear equations like 30k+1, 30k+7, 30k+11, 30k+13, 30k+17, 30k+19, 30k+23 and 30k+29 also have been used to produce pseudo primes. In this paper, an effort has been made to implement all three methods in implementation of RSA algorithm with large integers. A comparison has been made based on their time complexity and number of pseudo primes. It has been observed that the set of linear equations, have given better results compared to other methods.

ESTIMATION OF COMPLEXITY OF EFFECTIVE ALGORITHMS FOR CHECKING A PRESENCE OF JOINT ACTION OF BINARY FACTORS

2020 ◽  
Author(s):  
Yuliya Nagrebeckaya ◽  
Vladimir Panov
Keyword(s):  
Joint Action ◽  
Time Complexity ◽  
Input Data ◽  
The Given ◽  
Asymptotic Time

Effective algorithms are provided for checking presence of joint action of k factors in a given outcome which depends on n factors (k < n) and for calculation of degrees of that joint action for any k. It is demonstrated that asymptotic time complexity of the proposed algorithms does not exceed square of the input data size representing the given outcome

THE PERMUTATIONAL GRAPH: A NEW NETWORK TOPOLOGY

1998 ◽  
Vol 09 (01) ◽  
pp. 3-11
Author(s):  
SATOSHI OKAWA
Keyword(s):  
Network Topology ◽  
Equivalence Classes ◽  
Star Graph ◽  
Complete Graphs ◽  
Graph Topology ◽  
Star Graphs ◽  
Network Topologies ◽  
Graph Families ◽  
The Relationship ◽  
Better Than

This paper introduces the penmutational graph, a new network topology, which preserves the same desirable properties as those of a star graph topology. A permutational graph can be decomposed into subgraphs induced by node sets defined by equivalence classes. Using this decomposition, its structual properties as well as the relationship among graph families, permutational graphs, star graphs, and complete graphs are studied. Moreover, the diameters of permutational graphs are investigated and good estimates are obtained which are better than those of some network topologies of similar orders.

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