• Proceedings of the Korean Information Science Society Conference
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• 1998.10b
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• pp.661-663
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• 1998

합병 문제는 크기가 각각 l, m(l+m=n)인 두 개의 정렬된 리스트를 하나의 정렬된 리스트로 만드는 문제로 정렬 문제와 그래프 문제 등과 같은 여러 가지 문제를 해결하는데 필요한 중요한 문제이다. p($\theta${{{{ LEFT ( {λlogp} over {log(λ+1)} RIGHT ) }}}}).

• Journal of KIISE:Computer Systems and Theory
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• v.35 no.9_10
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• pp.476-484
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• 2008

Most string problems and their solutions are relevant to diverse applications such as pattern matching, data compression, recently bioinformatics, and so on. However, there have been few works on the relations between string problems and cryptographic problems. In this paper, we consider the following string reconstruction problems and show how these problems can be applied to cryptography. Given a string x of length n over a constant-sized alphabet ${\sum}$ and a set W of strings of lengths at most an integer $k({\leq}n)$, the first problem is to find the sequence of strings in W that reconstruct x by the minimum number of concatenations. We propose an O(kn+L)-time algorithm for this problem, where L is the sum of all lengths of strings in a given set, using suffix trees and a shortest path algorithm for directed acyclic graphs. The other is a dynamic version of the first problem and we propose an $O(k^3n+L)$-time algorithm. Finally, we show that exponentiation problems that arise in cryptography can be successfully reduced to these problems and propose a new solution for exponentiation.

• Journal of KIISE:Computer Systems and Theory
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• v.29 no.12
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• pp.640-647
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• 2002

In this paper, we consider the problems related to the edge visibility on a reconfigurable mesh(in short, RMESH). The following basic problems related to the edge visibility are considered: First, determine if a given polygon is visible from a specific edge, Second, find all edges from which a given polygon is visible. Third, compute the visibility polygon from a specific edge of a given polygon. In this paper, we consider the following problem in order to solve these problems in constant time: given two edges e and f of a simple polygon p, compute the maximal interval of f which is visible from e. We present a constant time algorithm for the problem on an N-N RMESH, where N is the number of vertices of P. Applying the algorithm, we can solve the above three problems in a constant time on a reconfigurable mesh. Specially, we can solve the third problem in a constant time on an N-$N_2$ RMESH.

• Journal of Industrial Convergence
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• v.19 no.4
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• pp.23-28
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• 2021

This paper finds the regular pattern of n = [3, ∞] for Euler square game related with n = 6(6×6=36) thirty-six officer problem that is still unsolved problem. The solution of this problem is exists for n = [3, 10] without n = 6. Also, previous researchers finds the random assigned solution for specific number using computer programming. Therefore, the solution of n = [11, ∞] Euler squares are unsolved problem because of anything but easy. This paper attempts to find generalized patterns for domains that have been extended to n = [3, ∞], while existing studies have been limited to n = [3, 10]. This paper classify the n = [3, ∞] into n = odd, 4k even, 4k+2 even of three classes. Then we find the simple regular pattern solution for n = odd and 4k even(n/2 = even). But we can't find the regular pattern for 4k+2 even(n/2 = odd).

• The KIPS Transactions:PartA
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• v.9A no.2
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• pp.225-230
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• 2002

The constrained off-line competitive deletion problem is a simple form of the set manipulation operations problem. It excludes the insertion operation from the off-line competitive deletion problem. An optimal sequential algorithm and a CREW PRAM algorithm which runs $O(log^2nloglogn)$ time using O(n/loglogn) processors were already presented in the literature. In this paper, we present a reconfigurable mesh algorithm for the constrained off-line competitive deletion problem. The proposed algorithm is executed in a constant time on an $n{\times}n$ reconfigurable mesh, and the result is $AT^2$ optimal.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2013.10a
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• pp.773-775
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• 2013

In this paper, we consider the problem for finding a vertex sequence of the directed cycle graph from the individual neighborhood information on a reconfigurable mesh(in short, RMESH). This problem can be solved in linear time using a sequential algorithm. However, it is difficult to develop a sublinear time parallel algorithm for the problem because of its sequential nature. All kinds of polygons can be represented by directed cycles, hence a solution of the problem may be used to solving problems in which a polygon should be constructed from the adjacency information for each vertex. In this paper, we present a constant time $n{\times}n^2$ RMESH algorithm for the problem with n vertices.

• Journal of KIISE:Computer Systems and Theory
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• v.36 no.1
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• pp.21-25
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• 2009

In this paper, we study the problem to fit a piecewise-quadratic polynomial curve to points in the plane. The curve consists of quadratic polynomial segments and two points are connected by a segment. But it passes through a subset of points, and for the points not to be passed, the error between the curve and the points is estimated in $L^{\infty}$ metric. We consider two optimization problems for the above problem. One is to reduce the number of segments of the curve, given the allowed error, and the other is to reduce the error between the curve and the points, while the curve has the number of segments less than or equal to the given integer. For the number n of given points, we propose $O(n^2)$ algorithm for the former problem and $O(n^3)$ algorithm for the latter.

• Journal of the Korea Society of Computer and Information
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• v.26 no.3
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• pp.111-117
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• 2021

The delivery problem on a graph is that of minimizing the object delivery time from one vertex to another vertex on a graph with m vertices using n various speed robot agents. In this paper, we propose two optimal solution algorithms for the delivery problem on a graph with time complexity of O(㎥n) and O(㎥). After preprocessing to obtain the shortest path for all pairs of the graph, our algorithm processed by obtaining the shortest delivery path in the order of the vertices with the least delivery time. Assuming that the graph reflects the terrain on which to solve the problem, our O(㎥) algorithm actually has a time complexity of O(㎡n) as only one preprocessing is required for the various deployment of n robot agents.

• Journal of KIISE:Computer Systems and Theory
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• v.31 no.3_4
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• pp.145-151
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• 2004

We present an efficient data structure to obtain the range minima in an away in constant time. Recently, suffix ways are extensively used to search DNA sequences fast in bioinformatics. In constructing suffix arrays, solving the range minima problem is necessary When we construct suffix arrays, we should solve the range minima problem not only in a time-efficient way but also in a space-efficient way. The reason is that DNA sequences consist of millions or billions of bases. Until now, the most efficient data structure to find the range minima in an way in constant time is based on the method that converts the range minima problem in an array into the LCA (Lowest Common Ancestor) problem in a Cartesian tree and then converts the LCA problem into the range minima problem in a specific array. This data structure occupies O( n) space and is constructed in O(n) time. However since this data structure includes intermediate data structures required to convert the range minima problem in an array into other problems, it requires large space (=13n) and much time. Our data structure is based on the method that directly solves the range minima problem. Thus, our data structure requires small space (=5n) and less time in practice. As a matter of course, our data structure requires O(n) time and space theoretically.

• Journal of the Korea Computer Industry Society
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• v.2 no.10
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• pp.1301-1308
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• 2001

In this paper, some interesting aspects of Grzegorczyk classes $\xi\sum{n}$, n$\geq$0 & $\sum$= { 1, 2 } of word-theoretic primitive recursive functions are observed including the classes of its corresponding predicates ($\xi\sum{n}$)* In particular, the small classes $\xi\sum{n}$($n\leq2$) are very incomparable to the corresponding small classes $\xi\sum{n}$ where $\xi\sum{n}$ is the number-theoretic Grzegorczyk classes. As one of some interesting aspects of the small classes, we show that the equivalence problem in $\xi\sum{0}$is undecidable.