• Journal of KIISE:Computer Systems and Theory
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• v.26 no.11
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• pp.1373-1381
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• 1999

이 논문에서는 통신망 설계 응용분야의 문제를 그래프 이론 문제로써 고려해 보았다. 개별 기업체가 서로 떨어진 두 곳을 연결하고자 할 때 공용통신망의 회선을 빌려 통신망을 구축하게 되는데 많은 경우 여러 종류의 회선들이 공급됨으로 어떤 회선을 선택하느냐의 문제가 생긴다. 일반적으로 빠른 회선(low delay)은 느린 회선(high delay)에 비해 비싸다. 그러나 서비스의 질(Quality of Service)이라는 요구사항이 종종 종단지연(end-to-end delay)시간에 의해 결정되므로, 무조건 낮은 가격의 회선만을 사용할 수는 없다. 결국 개별 기업체의 통신망을 위한 통로를 공용 통신망 위에 덮어씌워(overlaying) 구축하는 것의 여부는 두 개의 상반된 인자인 가격과 속도의 조절에 달려 있다. 따라서 일반적인 최소경로 찾기의 변형이라 할 수 있는 다음의 문제가 본 논문의 관심사이다. 두 개의 지점을 연결하는데 종단지연시간의 한계를 만족하면서 최소경비를 갖는 경로에 대한 해결을 위하여, 그래프 채색(coloring) 문제와 최단경로문제를 함께 포함하는 그래프 이론의 문제로 정형화시켜 살펴본다. 배낭문제로의 변환을 통해 이 문제는 {{{{NP-complete임을 증명하였고 {{{{O($\mid$E$\mid$D_0 )시간에 최적값을 주는 의사선형 알고리즘과O($\mid$E$\mid$)시간의 근사 알고리즘을 보였다. 특별한 경우에 대한 {{{{O($\mid$V$\mid$ + $\mid$E$\mid$)시간과 {{{{O($\mid$E$\mid$^2 + $\mid$E$\mid$$\mid$V$\mid$log$\mid$V$\mid$)시간 알고리즘을 보였으며 배낭 문제의 해결책과 유사한 그리디 휴리스틱(greedy heuristic) 알고리즘이 그물 구조(mesh) 그래프 상에서 좋은 결과를 보여주고 있음을 실험을 통해 확인해 보았다.Abstract This paper considers a graph-theoretic problem motivated by a telecommunication network optimization. When a private organization wishes to connect two sites by leasing physical lines from a public telecommunications network, it is often the cases that several categories of lines are available, at different costs. Typically a faster (low delay) lines costs more than a slower (high delay) line. However, low cost lines cannot be used exclusively because the Quality of Service (QoS) requirements often impose a bound on the end-to-end delay. Therefore, overlaying a path on the public network involves two diametrically opposing factors: cost and delay. The following variation of the standard shortest path problem is thus of interest: the shortest route between the two sites that meets a given bound on the end-to-end delay. For this problem we formulate a graph-theoretical problem that has both a shortest path component as well as coloring component. Interestingly, the problem could be formulated as a knapsack problem. We have shown that the general problem is NP-complete. The optimal polynomial-time algorithms for some special cases and one heuristic algorithm for the general problem are described.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.26 no.5
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• pp.1089-1097
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• 2016

It is well-known that, if additional information other than a plaintext-ciphertext pair is available, breaking the RSA cryptosystem may be much easier than factorizing the RSA modulus. For example, Coppersmith showed that, given the 1/2 fraction of the least or most significant bits of one of two RSA primes, the RSA modulus can be factorized in a polynomial time. More recently, Henecka et. al showed that the RSA private key of the form (p, q, d, $d_p$, $d_q$) can efficiently be recovered whenever the bits of the private key are erroneous with error rate less than 23.7%. It is notable that their algorithm is based on counting the matching bits between the candidate key bit string and the given decayed RSA private key bit string. And, extending the algorithm, this paper proposes a new RSA private key recovery algorithm using a generalized probabilistic measure for measuring the consistency between the candidate key bits and the given decayed RSA private key bits.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.38 no.4
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• pp.64-71
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• 2015

In this paper, we present a multi-period 0-1 knapsack problem which has the cardinality constraints. Theoretically, the presented problem can be regarded as an extension of the multi-period 0-1 knapsack problem. In the multi-period 0-1 knapsack problem, there are n jobs to be performed during m periods. Each job has the execution time and its completion gives profit. All the n jobs are partitioned into m periods, and the jobs belong to i-th period may be performed not later than in the i-th period, i = 1, ${\cdots}$, m. The total production time for periods from 1 to i is given by $b_i$ for each i = 1, ${\cdots}$, m, and the objective is to maximize the total profit. In the extended problem, we can select a specified number of jobs from each of periods associated with the corresponding cardinality constraints. As the extended problem is NP-hard, the branch and bound method is preferable to solve it, and therefore it is important to have efficient procedures for solving its linear programming relaxed problem. So we intensively explore the LP relaxed problem and suggest a polynomial time algorithm. We first decompose the LP relaxed problem into m subproblems associated with each cardinality constraints. Then we identify some new properties based on the parametric analysis. Finally by exploiting the special structure of the LP relaxed problem, we develop an efficient algorithm for the LP relaxed problem. The developed algorithm has a worst case computational complexity of order max[$O(n^2logn)$, $O(mn^2)$] where m is the number of periods and n is the total number of jobs. We illustrate a numerical example.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.23 no.6
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• pp.125-132
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• 2023

To NP-complete 3-SAT problem, this paper proposes a O(nm) polynomial time algorithm, where n is the number of literals and m is the total frequency of all literals in equation f. Conventionally well-known DPLLs should perform O(2^𝑙) in the worst case by performing backtracking if they fail to find a solution in a brute-force search of a branch-and-bound for the number of literals 𝑙. DPLL forms the core of the SAT Solver by substituting true(T) or false(F) for a literal so that a clause containing the least frequency literal is true(T) and removing a clause containing that literal. Contrary to DPLL, the proposed algorithm selects a literal _max𝑙 with the maximum frequency and sets $_{\max}({\mid}l{\mid},{\mid}{\bar{l}}{\mid})=1$. It then deletes 𝑙∈c_i clause in addition to ${\bar{l}}$ from ${\bar{l}}{\in}c_i$ clause. Its test results on various k-SAT problems not only show that it performs less than existing DPLL algorithm, but prove its simplicity in satisfiability verification.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.267-280
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• 2007

Various single-valued design optimality criteria such as D-, G-, and V-optimality are used often in constructing optimal experimental designs for mixture experiments in a constrained region R where lower and upper bound constraints are imposed on the ingredients proportions. Even though they are optimal in the strict sense of particular optimality criterion used, it is known that their performance is unsatisfactory with respect to the prediction capability over a constrained region. (Vining et at., 1993; Khuri et at., 1999) We assume the quadratic polynomial model as the mixture response surface model and are interested in finding efficient designs in the constrained design space for a mixture. In this paper, we make an expanded list of candidate design points by adding interior points to the extreme vertices, edge midpoints, constrained face centroids and the overall centroid. Then, we want to propose a robust design with respect to D-optimality, G-optimality, V-optimality and distance-based U-optimality. Comparing scaled prediction variance quantile plots (SPVQP) of robust designs with that of recommended designs in Khuri et al. (1999) and Vining et al. (1993) in the well-known examples of a four-component fertilizer experiment as well as McLean and Anderson's Railroad Flare Experiment, robust designs turned out to be superior to those recommended designs.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.3
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• pp.59-67
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• 2013

Reed-Solomon (RS) codes are powerful error-correcting codes used in diverse applications. Recently, algebraic soft-decision decoding algorithm for RS codes that can correct the errors beyond the error correcting bound has been proposed. The algorithm requires very intensive computations for interpolation, therefore an efficient VLSI architecture, which is realizable in hardware with a moderate hardware complexity, is mandatory for various applications. In this paper, we propose an efficient architecture with low hardware complexity for interpolation in soft-decision list decoding of Reed-Solomon codes. The proposed architecture processes the candidate polynomial in such a way that the terms of X degrees are processed in serial and the terms of Y degrees are processed in parallel. The processing order of candidate polynomials adaptively changes to increase the efficiency of memory access for coefficients; this minimizes the internal registers and the number of memory accesses and simplifies the memory structure by combining and storing data in memory. Also, the proposed architecture shows high hardware efficiency, since each module is balanced in terms of latency and the modules are maximally overlapped in schedule. The proposed interpolation architecture for the (255, 239) RS list decoder is designed and synthesized using the DongbuHitek $0.18{\mu}m$ standard cell library, the number of gate counts is 25.1K and the maximum operating frequency is 200 MHz.