• 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 Institute of Industrial Engineers
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• v.29 no.4
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• pp.253-258
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• 2003

We consider the problem of grouping orders into lots. The problem is modelled by a graph G=(V,E), where each node ${\nu}{\in}V$ denotes order specification and its weight ${\omega}(\nu)$ the orders on hand for the specification. We can construct a lot simply from orders of single specification. For a set of nodes (specifications) ${\theta}{\subseteq}V$, if the distance of any two nodes in $\theta$ is at most d, it is also possible to make a lot using orders on the nodes. The objective is to maximize the number of lots with size exactly $\lambda$. In this paper, we prove that our problem is NP-Complete when $d=2,{\lambda}=3$ and each weight is 0 or 1. Moreover, it is also shown to be NP-Complete when $d=1,{\lambda}=3$ and each weight is 1,2 or 3.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.12
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• pp.2865-2870
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• 2015

Recently, due to the hardware computing enhancement such as quantum computers, the amount of information that can be processed in a short period of time is growing exponentially. The cryptography system proposed by Koblitz and Fellows has a problem that it can not be guaranteed that the problem finding perfect dominating set is NP-complete in specific 3-regular graphs because the number of invariant polynomial can not be generated enough. In this paper, we propose an enhanced method to improve the vulnerability in 3-regular graph by generating plenty of invariant polynomials.

• Convergence Security Journal
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• v.14 no.7
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• pp.59-64
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• 2014

We investigate $p(n){\cdot}2^{O(\sqrt{n})}$ algorithm for 0/1 knapsack problem where x is the total bit length of a list of sizes of n objects. The algorithm is adaptable of method that achieves a similar complexity for the partition and Subset Sum problem. The method can be applied to other optimization or decision problem based on a list of numerics sizes or weights. 0/1 knapsack problem can be used to solve NP-Complete Problems with pseudo-polynomial time algorithm. We try to apply this technique to bio-informatics problem which has pseudo-polynomial time complexity.

• Journal of the Korea Society of Computer and Information
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• v.19 no.10
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• pp.169-173
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• 2014

Nobody has yet been able to determine the optimal solution conclusively whether NP-complete problems are in fact solvable in polynomial time. Gu$\acute{e}$ret et al. tries to obtain the optimal solution using linear programming with $O(m^4)$ time complexity for barge loading problem a kind of bin packing problem that is classified as nondeterministic polynomial time (NP)-complete problem. On the other hand, this paper suggests the loading rule of profit priority rank algorithm with O(m log m) time complexity. This paper decides the profit priority rank firstly. Then, we obtain the initial loading result using the rule of loading the good has profit priority order. Finally, we balance the loading and capability of barge swap the goods of unloading in previously loading in case of under loading. As a result of experiments, this algorithm reduces the $O(m^4)$ of linear programming to O(m log m) time complexity for NP-complete barge loading problem.

• Journal of the Korea Computer Industry Society
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• v.2 no.10
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• pp.1349-1354
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• 2001

In the Traveling Salesman Problem(TSP), a set of N cities is given and the problem is to find the shortest route connecting them all, with no city visited twice and return to the city at which it started. Since TSP is a well-known combinatorial optimization problem and belongs to the class of NP-complete problems, various techniques are required for finding optimum or near optimum solution to the TSP. Especially DNA computing, which uses real bio-molecules to perform computations supported by molecular biology, has been studied by many researchers to solve NP-complete problem using massive parallelism of DNA computing. Though very promising, DNA computing technology of today is inefficiency because the effective computing models and operations reflected the characteristics of bio-molecules have not been developed yet. In this paper, I design new Polymerase Chain Reaction(PCR) operations of DNA computing to solve TSP.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.5
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• pp.263-269
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• 2014

In this paper, I disprove Hadwiger conjecture of the vertex coloring problem, which asserts that "All $K_k$-minor free graphs can be colored with k-1 number of colors, i.e., ${\chi}(G)=k$ given $K_k$-minor." Pursuant to Hadwiger conjecture, one shall obtain an NP-complete k-minor to determine ${\chi}(G)=k$, and solve another NP-complete vertex coloring problem as a means to color vertices. In order to disprove Hadwiger conjecture in this paper, I propose an algorithm of linear time complexity O(V) that yields the exact solution to the vertex coloring problem. The proposed algorithm assigns vertex with the minimum degree to the Maximum Independent Set (MIS) and repeats this process on a simplified graph derived by deleting adjacent edges to the MIS vertex so as to finally obtain an MIS with a single color. Next, it repeats the process on a simplified graph derived by deleting edges of the MIS vertex to obtain an MIS whose number of vertex color corresponds to ${\chi}(G)=k$. Also presented in this paper using the proposed algorithm is an additional algorithm that searches solution of ${\chi}^{{\prime}{\prime}}(G)$, the total chromatic number, which also remains NP-complete. When applied to a $K_4$-minor graph, the proposed algorithm has obtained ${\chi}(G)=3$ instead of ${\chi}(G)=4$, proving that the Hadwiger conjecture is not universally applicable to all the graphs. The proposed algorithm, however, is a simple algorithm that directly obtains an independent set minor of ${\chi}(G)=k$ to assign an equal color to the vertices of each independent set without having to determine minors in the first place.

• Management Science and Financial Engineering
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• v.15 no.2
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• pp.69-100
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• 2009

In this paper, we consider a relatively new two-machine flow shop scheduling problem where the unit time WIP cost increases as a job passes through various stages in the production process, and the objective is to minimize the total WIP (work-in-process) cost. Specifically, we study three special cases of the problem. First, we consider the problem where processing times on machine 1 are identical. Second, the problem with identical processing times on machine 2 is examined. The recognition version of the both problems is unary NP-complete (or NP-complete in strong sense). For each problem, we suggest two simple and intuitive heuristics and find the worst case bound on relative error. Third, we consider the problem where the processing time of a job on each machine is proportional to a base processing time. For this problem, we show that a known heuristic finds an optimal schedule.

• Journal of the Korean Operations Research and Management Science Society
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• v.33 no.1
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• pp.35-49
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• 2008

To load a container in a yard block onto a ship, a Transfer Crane (TC) moves to a target yard bay, then its hoist picks up a selected container and loads it onto a waiting Yard Truck (YT). An optimal routing problem of Transfer Crane is a decision problem which determines a given TC's the visiting sequence of yard-bays and the number of containers to transfer from each yard-bay. The objective is to minimize the travel time of the TC between yard-bays and setup time for the TC in a visiting yard. In this paper, we shows that the problem is NP-complete, and suggests a new formulation for it. Using the new formulation for the problem, we investigate some characteristics of solutions, a lower and upper bounds for it. Moreover, our lower and upper bound is very efficient to applying some instances suggested in a previous work.

• Journal of the Korea Society of Computer and Information
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• v.20 no.4
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• pp.111-117
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• 2015

The exam scheduling problem has been classified as nondeterministic polynomial time-complete (NP-complete) problem because of the polynomial time algorithm to obtain the exact solution has been unknown yet. Gu${\acute{e}}$ret et al. tries to obtain the solution using linear programming with $O(m^4)$ time complexity for this problem. On the other hand, this paper suggests chromatic number algorithm with O(m) time complexity. The proposed algorithm converts the original data to incompatibility matrix for modules and graph firstly. Then, this algorithm packs the minimum degree vertex (module) and not adjacent vertex to this vertex into the bin $B_i$ with color $C_i$ in order to exam within minimum time period and meet the incompatibility constraints. As a result of experiments, this algorithm reduces the $O(m^4)$ of linear programming to O(m) time complexity for exam scheduling problem, and gets the same solution with linear programming.