hamiltonian paths
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Ergodesign ◽  
2021 ◽  
Vol 0 (3) ◽  
pp. 169-176
Author(s):  
Andrey Golovinsky

In this article, the object of research is the military personnel as a system, and the subject of research is the synergetic property of the system, namely the social psyche. The main objective of the study is to quantitatively describe the system microstatuses (the number of system elements, the maximum number of servicemen included in closed separate communication streams, the total number of these streams). At the macrolevel, a measure of the statistical uncertainty of the social psyche is calculated as a synergistic property of the system. The sociometry method (D.L. Moreno), graph theory and the algorithm for calculating Hamiltonian paths (N. Christophides) are used to identify any military personnel included in closed communication streams. Boltzmann's method of calculating the entropy is used as the initial entropy formula. As a result of the study, recommendations are obtained for restructuring the leadership style, using the tendencies towards organization and disorganization in the personnel making. The novelty of the article lies in formulating the problem of determining the measure of the statistical uncertainty of the social psyche, in proving the significance of the natural scientific approach in describing and identifying the elements of the system (military personnel) and in the quantitative description of the synergetic phenomena of a social group.


Author(s):  
Li-Yen Hsu

Holistic information integrity for managing wicked problems, developing equity is getting attention. Artifitial intelligence based topologies, dual sensor-information nodes, are prototyped to offer more availability, reliability, maintainability for operating healthy urbanism. Bipartite spider-webs, cube-connected cycles are aimed in ‘the radial-ring urban-building skeleton’ and ‘wetlands and sparsely populated areas’, respectively. Furthermore, honeycomb tori, mathematical HT(m), m≥2, for tasks related to wireless communications, are found having two mutually independent Hamiltonian paths (MIHP). This parallelism creates dual cipher-coding, supports logistic privacy, and help prevent information loss, electromagnetic interference, unexpected changes caused by such as clogged water.


2021 ◽  
Vol 10 (2) ◽  
pp. 115
Author(s):  
SYAMSYIDA ROZI ◽  
CUT MULTAHADAH

This research is related to the route of picking up the waste which done by janitors in housing complex of Aur Duri Indah Rt.14 Jambi considering the condition of that housing which have some crossroads, such that janitors take the same road twice which seems inefficient in terms of time and fuel consumption. This research is aimed to identify scientifically about the shortest and more efficient route which should be taken by janitors. This problem is considered as optimization problem through graph modelling. To check the efficient route, the existence of Hamiltonian Path of the graph is identified by using Depth-First Search method, and so is the shortest path. It is found that there are 39 Hamiltonian paths and the shortest path has total distance of 793.8 meter. By the existence of the shortest Hamiltonian Path, it is confirmed that janitors in housing complex of Aur Duri Indah Rt.14 can travel each road once with total distance is about 793.8 meter.


Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 916
Author(s):  
Armando Maya-López ◽  
Fran Casino ◽  
Agusti Solanas

The collection of personal data is exponentially growing and, as a result, individual privacy is endangered accordingly. With the aim to lessen privacy risks whilst maintaining high degrees of data utility, a variety of techniques have been proposed, being microaggregation a very popular one. Microaggregation is a family of perturbation methods, in which its principle is to aggregate personal data records (i.e., microdata) in groups so as to preserve privacy through k-anonymity. The multivariate microaggregation problem is known to be NP-Hard; however, its univariate version could be optimally solved in polynomial time using the Hansen-Mukherjee (HM) algorithm. In this article, we propose a heuristic solution to the multivariate microaggregation problem inspired by the Traveling Salesman Problem (TSP) and the optimal univariate microaggregation solution. Given a multivariate dataset, first, we apply a TSP-tour construction heuristic to generate a Hamiltonian path through all dataset records. Next, we use the order provided by this Hamiltonian path (i.e., a given permutation of the records) as input to the Hansen-Mukherjee algorithm, virtually transforming it into a multivariate microaggregation solver we call Multivariate Hansen-Mukherjee (MHM). Our intuition is that good solutions to the TSP would yield Hamiltonian paths allowing the Hansen-Mukherjee algorithm to find good solutions to the multivariate microaggregation problem. We have tested our method with well-known benchmark datasets. Moreover, with the aim to show the usefulness of our approach to protecting location privacy, we have tested our solution with real-life trajectories datasets, too. We have compared the results of our algorithm with those of the best performing solutions, and we show that our proposal reduces the information loss resulting from the microaggregation. Overall, results suggest that transforming the multivariate microaggregation problem into its univariate counterpart by ordering microdata records with a proper Hamiltonian path and applying an optimal univariate solution leads to a reduction of the perturbation error whilst keeping the same privacy guarantees.


2021 ◽  
pp. 120-126
Author(s):  
A. N. Rybalov ◽  

Generic-case approach to algorithmic problems has been offered by A. Miasnikov, V. Kapovich, P. Schupp, and V. Shpilrain in 2003. This approach studies an algorithm behavior on typical (almost all) inputs and ignores the rest of inputs. In this paper, we study the generic complexity of the problem of recognition of Hamiltonian paths in finite graphs. A path in graph is called Hamiltonian if it passes through all vertices exactly once. We prove that under the conditions P 6= NP and P = BPP for this problem there is no polynomial strongly generic algorithm. A strongly generic algorithm solves a problem not on the whole set of inputs, but on a subset, the sequence of frequencies of which exponentially quickly converges to 1 with increasing size. To prove the theorem, we use the method of generic amplification, which allows to construct generically hard problems from the problems hard in the classical sense. The main component of this method is the cloning technique, which combines the inputs of a problem together into sufficiently large sets of equivalent inputs. Equivalence is understood in the sense that the problem is solved similarly for them.


2020 ◽  
Vol 38 (02) ◽  
Author(s):  
CHUNG PHAM VAN

Checking integrity constraints in real-time the database is an important field of investigation. In this paper, we implement topological integrity constraints depending on which user has chosen an integrity constraint on different times on many existing integrity constraints of temporal databases. We suggested using the Hamiltonian paths in directed graphs order to implement a test program on data simulated by a college's real data. The object needs to satisfy integrity constraints in temporal databases as students who have enrolled in the subjects. Moreover, the program also monitors the learning process and advises students to choose courses in the school's training program.


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