• Title/Summary/Keyword: Polynomial Time Algorithm

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Branch-and-Bound Algorithm for Division of Perfect Nine Dart Combinations (퍼펙트 9 다트 조합의 나눗셈 분기한정 알고리즘)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.22 no.4
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    • pp.87-94
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    • 2022
  • This paper researched a study to find a combination of acquisition scores for 9 dart throws, which is the minimum number of dart tactile throws in 501 point dart games. The maximum score that can be obtained by throwing once in a dart game is 60 points, which can end the perfect dart game with 60 points eight times according to 60×8+21×1=501, and if you earn 21 points once, you can finish the game with 9 throws. This is called 9-dart finish. As such, only 18 and 14 studies on the combination of scores that can obtain 501 points with 9 throws are known, and no studies have been conducted applying the exhaustive search algorithm. This paper proposed a division branch-and-bound algorithm as a method of simplifying the O(2n) exponential time performance complexity of the typical branch-and-bound method of a exhaustive search method, to polynomial time complexity. The proposed method limited the level to 8, jumped to a quotient level of 501/60, and backtracked to explore only possible score combinations in the previous level. The possible score combinations of the nine perfect games found with the proposed algorithm were 90(101 cases).

Book Remodeling Analysis of Femur Using Hybrid Beam Theory (보 이론을 이용한 대퇴골 재생성의 해석)

  • Kim, Seung-Jong;Jeong, Jae-Yeon;Ha, Seong-Gyu
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.2 s.173
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    • pp.329-337
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    • 2000
  • An investigation has been performed to develop an analysis tool based on a nonlinear beam theory, which can be used to predict the long-term behavior of an artificial hip joint. The nonlinear behav ior of the femur arise from the coupled dependence of the bone density and the mechanical properties on each other. The beam theory together with its numerical algorithm is developed to take into account the nonlinear bone remodeling process of the femur that is long enough to be assumed as a beam. A piecewise linear curve for the bone remodeling rate is used in the bone remodeling theory and the surface area density of bone is modeled as the third order polynomial function of bone density. At each section of the beam, a constant curvature is assumed and the longitudinal strains are also assumed to vary linearly across the section. The Newton-Rhapson iteration method is used to solve the nonlinear equations for each cross section of the bone and a backward method is used to march along the time. The density and the remodeling signal ar, calculated along with time for the various time steps, and the developed beam theory has been verified by comparing with the results of finite element analysis of a remodeling bone with an artificial hip joint of titanium prosthesis subjected to uni-axial loads and pure bending moment. It is concluded that the developed beam theory can be used to predict the long-term behavior of the femur and thus to design the artificial hip prosthesis.

Assessing the Vulnerability of Network Topologies under Large-Scale Regional Failures

  • Peng, Wei;Li, Zimu;Liu, Yujing;Su, Jinshu
    • Journal of Communications and Networks
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    • v.14 no.4
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    • pp.451-460
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    • 2012
  • Natural disasters often lead to regional failures that can cause network nodes and links co-located in a large geographical area to fail. Novel approaches are required to assess the network vulnerability under such regional failures. In this paper, we investigate the vulnerability of networks by considering the geometric properties of regional failures and network nodes. To evaluate the criticality of node locations and determine the critical areas in a network, we propose the concept of ${\alpha}$-critical-distance with a given failure impact ratio ${\alpha}$, and we formulate two optimization problems based on the concept. By analyzing the geometric properties of the problems, we show that although finding critical nodes or links in a pure graph is a NP-complete problem, the problem of finding critical areas has polynomial time complexity. We propose two algorithms to deal with these problems and analyze their time complexities. Using real city-level Internet topology data, we conducted experiments to compute the ${\alpha}$-critical-distances for different networks. The computational results demonstrate the differences in vulnerability of different networks. The results also indicate that the critical area of a network can be estimated by limiting failure centers on the locations of network nodes. Additionally, we find that with the same impact ratio ${\alpha}$, the topologies examined have larger ${\alpha}$-critical-distances when the network performance is measured using the giant component size instead of the other two metrics. Similar results are obtained when the network performance is measured using the average two terminal reliability and the network efficiency, although computation of the former entails less time complexity than that of the latter.

A Dynamic Piecewise Prediction Model of Solar Insolation for Efficient Photovoltaic Systems (효율적인 태양광 발전량 예측을 위한 Dynamic Piecewise 일사량 예측 모델)

  • Yang, Dong Hun;Yeo, Na Young;Mah, Pyeongsoo
    • KIISE Transactions on Computing Practices
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    • v.23 no.11
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    • pp.632-640
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    • 2017
  • Although solar insolation is the weather factor with the greatest influence on power generation in photovoltaic systems, the Meterological Agency does not provide solar insolation data for future dates. Therefore, it is essential to research prediction methods for solar insolation to efficiently manage photovoltaic systems. In this study, we propose a Dynamic Piecewise Prediction Model that can be used to predict solar insolation values for future dates based on information from the weather forecast. To improve the predictive accuracy, we dynamically divide the entire data set based on the sun altitude and cloudiness at the time of prediction. The Dynamic Piecewise Prediction Model is developed by applying a polynomial linear regression algorithm on the divided data set. To verify the performance of our proposed model, we compared our model to previous approaches. The result of the comparison shows that the proposed model is superior to previous approaches in that it produces a lower prediction error.

p-Facility Location Models (p-시설물 위치선정 모델)

  • Choi, Myeong-Bok;Lee, Sang-Un;Kim, Bong-Gyung;Joung, Seung-Sam;Han, Tae-Yong
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.11 no.6
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    • pp.193-205
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    • 2011
  • This paper suggests $p$-facility locations in $m$ candidate locations and $n$ areas in optimal cost side(population${\times}$shortest distance). This problem has been classified by NP-complete because there is not a polynomial time algorithm. In this paper, we suggests reverse-delete method that deletes a candidate facility one by one from $p=m$ until $p=2$. As a result of the proposed algorithm for the $5{\times}5$ and $7{\times}7$, the initial solution is obtained. For the Swain's 55-node network, we obtain the optimal solution through a solution improvement process with $p=4$ and it by using the initial solution with $p=5$.

An Energy Harvesting Aware Routing Algorithm for Hierarchical Clustering Wireless Sensor Networks

  • Tang, Chaowei;Tan, Qian;Han, Yanni;An, Wei;Li, Haibo;Tang, Hui
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.10 no.2
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    • pp.504-521
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    • 2016
  • Recently, energy harvesting technology has been integrated into wireless sensor networks to ameliorate the nodes' energy limitation problem. In theory, the wireless sensor node equipped with an energy harvesting module can work permanently until hardware failures happen. However, due to the change of power supply, the traditional hierarchical network routing protocol can not be effectively adopted in energy harvesting wireless sensor networks. In this paper, we improve the Low-Energy Adaptive Clustering Hierarchy (LEACH) protocol to make it suitable for the energy harvesting wireless sensor networks. Specifically, the cluster heads are selected according to the estimation of nodes' harvested energy and consumed energy. Preference is given to the nodes with high harvested energy while taking the energy consumption rate into account. The utilization of harvested energy is mathematically formulated as a max-min optimization problem which maximizes the minimum energy conservation of each node. We have proved that maximizing the minimum energy conservation is an NP-hard problem theoretically. Thus, a polynomial time algorithm has been proposed to derive the near-optimal performance. Extensive simulation results show that our proposed routing scheme outperforms previous works in terms of energy conservation and balanced distribution.

An Optimal Allocation Mechanism of Location Servers in A Linear Arrangement of Base Stations (선형배열 기지국을 위한 위치정보 서버의 최적할당 방식)

  • Lim, Kyung-Shik
    • The Transactions of the Korea Information Processing Society
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    • v.7 no.2
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    • pp.426-436
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    • 2000
  • Given a linear arrangement of n base stations which generate multiple types of traffic among themselves, we consider the problem of finding a set of disjoint clusters to cover n base statons so that a cluster is assigned a location server. Our goal is to minimize the total communication cost for the entire network where the cost of intra-cluster communication is usually lower than that of intercluster communication for each type of traffic. The optimization problem is transformed into an equivavalent problem using the concept of relative cost, which generates the difference of communication costs between intracluster and intercluster communications. Using the relative cost matrix, an efficient algorithm of O($mm^2$), where m is the number of clusters in a partition, is designed by dynamic programming. The algorithm also finds all thevalid partitions in the same polynomial time, given the size constraint on a cluster, and the total allowable communication cost for the entire network.

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Notes On Inverse Interval Graph Coloring Problems

  • Chung, Yerim;Kim, Hak-Jin
    • Journal of the Korea Society of Computer and Information
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    • v.24 no.10
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    • pp.57-64
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    • 2019
  • In this paper, we study a polynomially solvable case of the inverse interval graph coloring problem. Given an interval graph associated with a specific interval system, the inverse interval graph coloring problem is defined with the assumption that there is no proper K-coloring for the given interval graph, where K is a fixed integer. The problem is to modify the system of intervals associated with the given interval graph by shifting some of the intervals in such a way that the resulting interval graph becomes K-colorable and the total modification is minimum with respect to a certain norm. In this paper, we focus on the case K = 1 where all intervals associated with the interval graph have length 1 or 2, and interval displacement is only allowed to the righthand side with respect to its original position. To solve this problem in polynomial time, we propose a two-phase algorithm which consists of the sorting and First Fit procedure.

Analysis of Attacks and Security Level for Multivariate Quadratic Based Signature Scheme Rainbow (다변수 이차식 기반 서명 기법 Rainbow의 공격 기법 및 보안강도 분석)

  • Cho, Seong-Min;Kim, Jane;Seo, Seung-Hyun
    • Journal of the Korea Institute of Information Security & Cryptology
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    • v.31 no.3
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    • pp.533-544
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    • 2021
  • Using Shor algorithm, factoring and discrete logarithm problem can be solved effectively. The public key cryptography, such as RSA and ECC, based on factoring and discrete logarithm problem can be broken in polynomial time using Shor algorithm. NIST has been conducting a PQC(Post Quantum Cryptography) standardization process to select quantum-resistant public key cryptography. The multivariate quadratic based signature scheme, which is one of the PQC candidates, is suitable for IoT devices with limited resources due to its short signature and fast sign and verify process. We analyzes classic attacks and quantum attacks for Rainbow which is the only multivatiate quadratic based signature scheme to be finalized up to the round 3. Also we compute the attack complexity for the round 3 Rainbow parameters, and analyzes the security level of Rainbow, one of the PQC standardization candidates.

Short-term Scheduling Optimization for Subassembly Line in Ship Production Using Simulated Annealing (시뮬레이티드 어닐링을 활용한 조선 소조립 라인 소일정계획 최적화)

  • Hwang, In-Hyuck;Noh, Jac-Kyou;Lee, Kwang-Kook;Shin, Jon-Gye
    • Journal of the Korea Society for Simulation
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    • v.19 no.1
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    • pp.73-82
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    • 2010
  • Productivity improvement is considered as one of hot potato topics in international shipyards by the increasing amount of orders. In order to improve productivity of lines, shipbuilders have been researching and developing new work method, process automation, advanced planning and scheduling and so on. An optimization approach was accomplished on short-term scheduling of subassembly lines in this research. The problem of subassembly line scheduling turned out to be a non-deterministic polynomial time problem with regard to SKID pattern’s sequence and worker assignment to each station. The problem was applied by simulated annealing algorithm, one of meta-heuristic methods. The algorithm was aimed to avoid local minimum value by changing results with probability function. The optimization result was compared with discrete-event simulation's to propose what pros and cons were. This paper will help planners work on scheduling and decision-making to complete their task by evaluation.