• Title/Summary/Keyword: NP-complete 문제

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Sequential Longest Section Color Winning Algorithm for Car Paint Sequencing Problem (자동차 페인트 순서 문제의 연속된 최장 구간 색 승리 알고리즘)

  • Lee, Sang-Un
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.20 no.1
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    • pp.177-186
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    • 2020
  • This paper deals with the car paint sequencing problem (CPSP) that the entrance sequence is to same colored group with maximum sequenced cars for the buffer arriving cars from the body shop. This problem classified by NP-complete problem because of the exact solution has not obtained within polynomial time. CPSP is aim to minimum pugging number that each pugging must be performs at color changing time in order to entirely cleaning the remaining previous color. To be obtain the minimum number of moving distance with window concept and minimum number of pugging, this paper sorts same color and arriving sequence. Then we basically decide the maximum length section color time to winner team using stage race method. For the case of the loser team with no more racing or yield to loser team and more longer stage in upcoming racing, the winner team give way to loser team. As a result, all cars(runners) are winner in any stage without fail. For n cars, the proposed algorithm has a advantage of simple and fast with O(nlogn) polynomial time complexity, this algorithm can be get the minimum number of moving distance and purging for all of experimental data.

A Polynomial Time Algorithm for Vertex Coloring Problem (정점 색칠 문제의 다항시간 알고리즘)

  • Lee, Sang-Un;Choi, Myeong-Bok
    • Journal of the Korea Society of Computer and Information
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    • v.16 no.7
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    • pp.85-93
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    • 2011
  • The Vertex Coloring Problem hasn't been solved in polynomial time, so this problem has been known as NP-complete. This paper suggests linear time algorithm for Vertex Coloring Problem (VCP). The proposed algorithm is based on assumption that we can't know a priori the minimum chromatic number ${\chi}(G)$=k for graph G=(V,E) This algorithm divides Vertices V of graph into two parts as independent sets $\overline{C}$ and cover set C, then assigns the color to $\overline{C}$. The element of independent sets $\overline{C}$ is a vertex ${\upsilon}$ that has minimum degree ${\delta}(G)$ and the elements of cover set C are the vertices ${\upsilon}$ that is adjacent to ${\upsilon}$. The reduced graph is divided into independent sets $\overline{C}$ and cover set C again until no edge is in a cover set C. As a result of experiments, this algorithm finds the ${\chi}(G)$=k perfectly for 26 Graphs that shows the number of selecting ${\upsilon}$ is less than the number of vertices n.

Generalized K Path Searching in Seoul Metropolitan Railway Network Considering Entry-Exit Toll (진입-진출 요금을 반영한 수도권 도시철도망의 일반화 K-경로탐색)

  • Meeyoung Lee
    • The Journal of The Korea Institute of Intelligent Transport Systems
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    • v.21 no.6
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    • pp.1-20
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    • 2022
  • The basic way to charge vehicles for using road and public transport networks is the entry-exit toll system. This system works by reading Hi-Pass and public transportation cards of the vehicles using card readers. However, the problems of navigating a route in consideration of entry-exit toll systems include the non-additive costs of enumerating routes. This problem is known as an NP-complete task that enumerates all paths and derives the optimal path. So far, the solution to the entry-exit toll system charging has been proposed in the form of transforming the road network. However, unlike in the public transport network where the cards are generalized, this solution has not been found in situations where network expansion is required with a transfer, multi-modes and multiple card readers. Hence, this study introduced the Link Label for a public transportation network composed of card readers in which network expansion is bypassed in selecting the optimal path by enumerating the paths through a one-to-one k-path search. Since the method proposed in this study constructs a relatively small set of paths, finding the optimal path is not burdensome in terms of computing power. In addition, the ease of comparison of sensitivity between paths indicates the possibility of using this method as a generalized means of deriving an optimal path.

Path Algorithm for Maximum Tax-Relief in Maximum Profit Tax Problem of Multinational Corporation (다국적기업 최대이익 세금트리 문제의 최대 세금경감 경로 알고리즘)

  • Sang-Un Lee
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.23 no.4
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    • pp.157-164
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    • 2023
  • This paper suggests O(n2) polynomial time heuristic algorithm for corporate tax structure optimization problem that has been classified as NP-complete problem. The proposed algorithm constructs tax tree levels that the target holding company is located at root node of Level 1, and the tax code categories(Te) 1,4,3,2 are located in each level 2,3,4,5 sequentially. To find the maximum tax-relief path from source(S) to target(T), firstly we connect the minimum witholding tax rate minrw(u, v) arc of node u point of view for transfer the profit from u to v node. As a result we construct the spanning tree from all of the source nodes to a target node, and find the initial feasible solution. Nextly, we find the alternate path with minimum foreign tax rate minrfi(u, v) of v point of view. Finally we choose the minimum tax-relief path from of this two paths. The proposed heuristic algorithm performs better optimal results than linear programming and Tabu search method that is a kind of metaheuristic method.

An Efficient Evolutionary Algorithm for the Fixed Charge Transportation Problem (고정비용 수송문제를 위한 효율적인 진화 알고리듬)

  • Soak, Sang-Moon;Chang, Seok-Cheoul;Lee, Sang-Wook;Ahn, Byung-Ha
    • Journal of Korean Institute of Industrial Engineers
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    • v.31 no.1
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    • pp.79-86
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    • 2005
  • The transportation problem (TP) is one of the traditional optimization problems. Unlike the TP, the fixed charge transportation problem (FCTP) cannot be solved using polynomial time algorithms. So, finding solutions for the FCTP is a well-known NP-complete problem involving an importance in a transportation network design. So, it seems to be natural to use evolutionary algorithms for solving FCTP. And many evolutionary algorithms have tackled this problem and shown good performance. This paper introduces an efficient evolutionary algorithm for the FCTP. The proposed algorithm can always generate feasible solutions without any repair process using the random key representation. Especially, it can guide the search toward the basic solution. Finally, we performed comparisons with the previous results known on the benchmark instances and could confirm the superiority of the proposed algorithm.

향상된 Approximated Vertex Cover(VC)을 이용한 AS망에서의 D-DoS 공격의 효율적 차단

  • Lee, Hoon-Jae;Jang, Ju-Wook
    • Proceedings of the Korean Information Science Society Conference
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    • 2004.04a
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    • pp.628-630
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    • 2004
  • Distributed Denial of Service(D-DoS) 공격을 차단하기 위해서는 AS(Autonomous System) 경계 라우터에 필터를 설치하는 것이 필요하다. 필터가 설치되는 라우터의 개수를 최소로 하는 Vertex Cover(VC)--모든 edge를 커버하는 Vertex의 모임--을 찾아내는 방법은 NP-complete 문제가 된다. 따라서 Vertex Cover(VC) 근사기법 중에서 Greedy 알고리즘과 Approximated VC 알고리즘에 대해 Vertex Cover(VC)을 찾아내는 방법을 적용하여 실험하였다. Vertex Cover(VC)를 찾을 경우 Worst case에서 이론상 VC수의 최대 2배의 Vertex Cover(VC)를 찾아낼 수 있는 Approximated VC 알고리즘의 장점과 적은 수의 Vertex Cover(VC)로 모든 edge를 커버할 수 있는 Greedy 알고리즘[7]의 장점을 모두 갖춘 Vertex Cover(VC) 근사 기법을 구현하였다. NS-2를 이용한 실험 결과, 제안된 알고리즘은 Greedy 알고리즘보다 Vertex Cover를 찾아가는 단계 수에 따른 커버되는 층 노드 수를 비교하였을 때. 전체 노드의 75%를 커버하는데 24번의 단계가 필요하여 Greedy 알고리즘의 40개 보다 40%의 단계의 수적인 감소가 일어났으며 전체노드의 90%를 커버하는데 38%의 단계 개수의 감소가 일어났다. 실험으로 제안된 알고리즘이 Vertex Cover(VC) 톨 찾아가는 단계 측면에서 좀더 빠르게 AS 경계 라우터에 필터를 설치하여 D-DoS에 효율적으로 대처해 나갈 수 있음을 확인할 수 있다.

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New Branching Criteria for the Asymmetric Traveling Salesman Problem (비대칭 외판원 문제를 위한 새로운 분지기법)

  • 지영근;강맹규
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.19 no.39
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    • pp.9-18
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    • 1996
  • Many algorithms have been developed for optimizing the asymmectric traveling salesman problem known as a representative NP-Complete problem. The most efficient ones of them are branch and bound algorithms based on the subtour elimination approach. To increase efficiency of the branch and bound algorithm. number of decision nodes should be decreased. For this the minimum bound that is more close at the optimal solution should be found or an effective bounding strategy should be used. If the optimal solution has been known, we may apply it usefully to branching. Because a good feasible solution should be found as soon as possible and have similar features of the optimal solution. By the way, the upper bound solution in branch and bound algorithm is most close at the optimal solution. Therefore, the upper bound solution can be used instead of the optimal solution and information of which can be applied to new branching criteria. As mentioned above, this paper will propose an effective branching rule using the information of the upper bound solution in the branch and bound algorithm. And superiority of the new branching rule will be shown by comparing with Bellmore-Malone's one and carpaneto-Toth's one that were already proposed.

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Improved approach of calculating the same shape in graph mining (그래프 마이닝에서 그래프 동형판단연산의 향상기법)

  • No, Young-Sang;Yun, Un-Il;Kim, Myung-Jun
    • Journal of the Korea Society of Computer and Information
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    • v.14 no.10
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    • pp.251-258
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    • 2009
  • Data mining is a method that extract useful knowledges from huge size of data. Recently, a focussing research part of data mining is to find interesting patterns in graph databases. More efficient methods have been proposed in graph mining. However, graph analysis methods are in NP-hard problem. Graph pattern mining based on pattern growth method is to find complete set of patterns satisfying certain property through extending graph pattern edge by edge with avoiding generation of duplicated patterns. This paper suggests an efficient approach of reducing computing time of pattern growth method through pattern growth's property that similar patterns cause similar tasks. we suggest pruning methods which reduce search space. Based on extensive performance study, we discuss the results and the future works.

Routing for Enhancing Source-Location Privacy with Low Delivery Latency in Sensor Networks (센서 네트워크에서 낮은 전달 지연으로 근원지 위치 기밀을 강화하는 라우팅)

  • Tscha, Yeong-Hwan
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.33 no.8B
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    • pp.636-645
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    • 2008
  • Most of routing schemes that protect the source's location from a malicious attacker usually make use of a path of a long length per message for the sake of lengthening the safety period. The biggest problem to such approaches is taking a very long latency in transferring messages to the destination. In this paper we show the problem to find the least-cost single path that is enough to keep the source-location always secure from the attacker, provided that it is used for the delivery of a set of messages given in priori, is NP-complete. Consequently we propose a routing protocol GSLP-w(GPSR-based Source-Location Privacy with crew size co) that is a trade-off between two extreme approaches. The advantage of GSLP-co lies in its enhanced safety period for the source and its lowered delivery latency in messaging. We consider NSP(Normalized Sefety Period) and NDL(Normalized Delivery Latency), measured in terms of the least number of hops to the destination, to achieve tangible interpretation of the results. We ran a simulation to confirm our claim by generating 100 topologies of 50,000 nodes with the average number of neighbors being 8. The results show that GSLP-$\omega$ provides more enhanced NSP compared to other protocols GSLP, an earlier version of GSLP-$\omega$, and PR-SP(Phantom Routing - Single Path), the most notable existing protocol for the source-location privacy, and less NDL than that of GSLP but more than that of PR-SP.

An Index Structure for Substructure Searching In Chemical Databases (화학 데이타베이스에서 부분구조 검색을 위한 인덱스 구조)

  • Lee Hwangu;Cha Jaehyuk
    • Journal of KIISE:Databases
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    • v.31 no.6
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    • pp.641-649
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    • 2004
  • The relationship between chemical structures and biological activities is researched briskly in the area of 'Medicinal Chemistry' At the base of these structure-based drug design tries, medicinal chemists search the existing drugs of similar chemical structure to target drug for the development of a new drug. Therefore, it is such necessary that an automatic system selects drug files that have a set of chemical moieties matching a user-defined query moiety. Substructure searching is the process of identifying a set of chemical moieties that match a specific query moiety. Testing for substructure searching was developed in the late 1950s. In graph theoretical terms, this problem corresponds to determining which graphs in a set are subgraph isomorphic to a specified query moiety. Testing for subgraph isomorphism has been proved, in the general case, to be an NP- complete problem. For the purpose of overcoming this difficulty, there were computational approaches. On the 1990s, a US patent has been granted on an atom-centered indexing scheme, used by the RS3 system; this has the virtue that the indexes generated can be searched by direct text comparison. This system is commercially used(http://www.acelrys.com/rs3). We define the RS3 system's drawback and present a new indexing scheme. The RS3 system treats substructure searching with substring matching by means of expressing chemical structure aspredefined strings. However, it has insufficient 'rerall' and 'precision‘ because it is impossible to index structures uniquely for same atom and same bond. To resolve this problem, we make the minimum-cost- spanning tree for one centered atom and describe a structure with paths per levels. Expressing 2D chemical structure into 1D a string has limit. Therefore, we break 2D chemical structure into 1D structure fragments. We present in this paper a new index technique to improve recall and precision surprisingly.