• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.2079-2082
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• 2002

An interconnection network is called hamiltonian-connected if there exists a hamiltonian path joining every pair of nodes. We consider the problem of adding edges to a mesh to make it hamiltonian- connected. We show that at least two edges are necessary for the problem. Also, we present the method to add two edges to a mesh so that the resulting network is hamiltonian-connected.

• International Journal of Computer Science & Network Security
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• v.21 no.8
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• pp.17-27
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• 2021

Non-abelian group based cryptosystems are a latest research inspiration, since they offer better security due to their non-abelian properties. In this paper, we propose a novel approach to non-abelian group based public-key cryptographic protocols using semidirect products of finite groups. An intractable problem of determining automorphisms and generating elements of a group is introduced as the underlying mathematical problem for the suggested protocols. Then, we show that the difficult problem of determining paths and cycles of Cayley graphs including Hamiltonian paths and cycles could be reduced to this intractable problem. The applicability of Hamiltonian paths, and in fact any random path in Cayley graphs in the above cryptographic schemes and an application of the same concept to two previous cryptographic protocols based on a Generalized Discrete Logarithm Problem is discussed. Moreover, an alternative method of improving the security is also presented.

• Proceedings of the Korean Information Science Society Conference
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• 2002.10d
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• pp.241-243
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• 2002

DNA 컴퓨팅은 생체 분자들이 갖는 막대한 병렬성을 정보 처리 기술에 적용한 기술이다. Adleman의 DNA 컴퓨팅은 랜덤한 고정길이의 형태로 문제를 표현하기 때문에 해를 찾지 못하거나 시간이 많이 걸리는 단점을 갖고 있다. 본 논문은 DNA 컴퓨팅에 DNA 코딩 방법을 적용하여 DNA 서열을 효율적으로 표현하고 반응횟수 만큼 합성과 분리 과정을 거쳐 최적의 코드를 생성하는 ACO(Algorithm for Code Optimization)를 제안한다. DNA 코딩 방법은 변형된 유전자 알고리즘으로 DNA 기능을 유지하며, 서열의 길이를 줄일 수 있으므로 최적의 서열을 생성할 수 있는 특징을 갖는다. ACO를 NP-complete 문제 중 Hamiltonian path problem에 적용하여 실험한 결과, Adleman의 DNA 컴퓨팅 보다 초기 문제 표현에서 높은 적합도 값을 갖는 서열을 생성했으며, 경로의 변화에도 능동적으로 대처하여 최적의 결과를 빠르게 탐색할 수 있었다.

• Journal of KIISE:Software and Applications
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• v.31 no.4
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• pp.387-393
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• 2004

DNA computing is technology that applies immense parallel castle of living body molecules into information processing technology, and has used to solve NP-complete problems. However, there are problems which do not look for solutions and take much time when only DNA computing technology solves NP-complete problems. In this paper we proposed an algorithm called ACO(Algorithm for Code Optimization) that can efficiently express DNA sequence and create good codes through composition and separation processes as many as the numbers of reaction by DNA coding method. Also, we applied ACO to Hamiltonian path problem of NP-complete problems. As a result, ACO could express DNA codes of variable lengths more efficiently than Adleman's DNA computing algorithm could. In addition, compared to Adleman's DNA computing algorithm, ACO could reduce search time and biological error rate by 50% and could search for accurate paths in a short time.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.23 no.59
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• pp.1-10
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• 2000

The traveling salesman problem is a representative NP-Complete problem. It needs lots of time to get a solution as the number of city increase. So, we need an efficient heuristic algorithm that gets good solution in a short time. Almost edges that participate in optimal path have somewhat low value cost. This paper discusses the property of nearest neighbor and 3-opt. This paper uses nearest neighbor's property to select candidate edge. Candidate edge is a set of edge that has high probability to improve cycle path. We insert edge that is one of candidate edge into intial cycle path. As two cities are connected. It does not satisfy hamiltonian cycle's rule that every city must be visited and departed only one time. This paper uses 3-opt's method to sustain hamiltonian cycle while inserting edge into cycle path. This paper presents a highly efficient heuristic algorithm verified by numerous experiments.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.12
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• pp.691-698
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• 2003

In this paper, we propose a problem, called one-to-one disjoint path cover problem, whether or not there exist k disjoint paths joining a pair of vertices which pass through all the vertices other than the two exactly once. A graph which for an arbitrary k, has a one-to-one disjoint path cover between an arbitrary pair of vertices has a hamiltonian property stronger than hamiltonian-connectedness. We investigate this problem on recursive circulants and prove that for an arbitrary k $k(1{\leq}k{\leq}m)$$ G(2^m,4)$,$m{\geq}3$, has a one-to-one disjoint path cover consisting of k paths between an arbitrary pair of vortices.

• International Journal of Computer Science & Network Security
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• v.21 no.4
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• pp.289-300
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• 2021

Non-abelian group based Cryptography is a field which has become a latest trend in research due to increasing vulnerabilities associated with the abelian group based cryptosystems which are in use at present and the interesting algebraic properties associated that can be thought to provide higher security. When developing cryptographic primitives based on non-abelian groups, the researchers have tried to extend the similar layouts associated with the traditional underlying mathematical problems and assumptions by almost mimicking their operations which is fascinating even to observe. This survey contributes in highlighting the different analogous extensions of traditional assumptions presented by various authors and a set of open problems. Further, suggestions to apply the Hamiltonian Cycle/Path Problem in a similar direction is presented.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.49.3-49
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• 2001

In 1994 Adelman´s pioneer work demonstrated that deoxyribonucleic acid (DNA) could be used as a medium for computation to solve mathematical problems. He described the use of DNA based computational approach to solve the Hamiltonian Path Problem (HPP). Since then a number of combinatorial problems have been analyzed by DNA computation approaches including, for example: Maximum Independent Set (MIS), Maximal Clique and Satisfaction (SAT) Problems. In the present paper we propose a method of solving another classic combinatorial optimization problem - the eraph Coloring Problem (GCP), using specifically designed circular DNA plasmids as a computation tool. The task of the analysis is to color the graph so that no two nodes ...

• Journal of the Korea Society of Computer and Information
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• v.20 no.5
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• pp.31-39
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• 2015

The degree-constrained minimum spanning tree (d-MST) problem is considered NP-complete for no exact solution-yielding polynomial algorithm has been proposed to. One thus has to resort to an heuristic approximate algorithm to obtain an optimal solution to this problem. This paper therefore presents a polynomial time algorithm which obtains an intial solution to the d-MST with the help of Kruskal's algorithm and performs k-opt on the initial solution obtained so as to derive the final optimal solution. When tested on 4 graphs, the algorithm has successfully obtained the optimal solutions.

• Journal of Digital Contents Society
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• v.18 no.6
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• pp.1119-1125
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• 2017

Genres and actions of stories can be used to classify stories, and used effectively as well for visualizing story properties. This paper proposes a Genre-Action coordinate system for visualizing story property data in 2-dimension that has similarities between the genre and action items along the axes, i.e. a property of spatial continuum. With the proposed Genre-Action coordinate system we found that the genre and action items in the axes are arranged according to their similarities and we were able to achieve a spatially meaningful visualization of story properties where the related data form clusters.