• Title/Summary/Keyword: Cardinality Constraint

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On overlapping territories satisfying cardinality constraints

  • Takashi Moriizumi;Shuji Tsukiyama;Shoji Shi Noda;Masakazu Sengoku;Isao Shirakawa
    • 제어로봇시스템학회:학술대회논문집
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    • 1987.10a
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    • pp.857-862
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    • 1987
  • Given a network with k specified vertices bi called centers, a cardinality constrained cover is a family {Bi} of k subsets covering the vertex set of a network, such that each subset Bi corresponds to and contains center bi, and satisfies a given cardinality constraint. A set of cardinality constrained overlapping territories is a cardinality constrained cover such that the total sum of T(B$_{i}$) for all subsets is minimum among all cardinality constrained covers, where T(B$_{i}$) is the summation of the shortest path lengths from center bi to every vertex in B$_{I}$. This paper considers a problem of finding a set of cardinality constrained overlapping territories. and proposes an algorithm for the Problem which has the time and space complexities are O(k$^{3}$$\mid$V$\mid$$^{2}$) and O(k$\mid$V$\mid$+$\mid$E$\mid$), respectively, where V and E are the sets of vertices and edges of a given network, respectively. The concept of overlapping territories has a possibility to be applied to a job assignment problem.oblem.

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Comparative Analysis on CNF Encodings for Boolean Cardinality Constraints (이진 변수 기수 조건을 위한 CNF 변환 방법의 분석)

  • Lee, Min;Kwon, Gi-Hwon
    • Journal of KIISE:Software and Applications
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    • v.35 no.2
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    • pp.81-90
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    • 2008
  • BCC(Boolean Cardinality Constraint) is to select one boolean variable from n different variables. It is widely used in many areas including software engineering. Thus, many efficient encoding techniques of BCC into CNF have been studied extensively In this paper we analyze some representative encodings with respect to flexibility as well as efficiency. In addition we use a visualization tool to draw the CNF clauses generated from each encodings. Visualizing the clauses exposes a hidden structure in encodings and makes to compare each encodings on the structure level, which is one of the prominent achievement in our work compared to other works. And we apply our analysis on the pigeon-hole problems to have confidence. In our experimental settings, the commander encoding shows the best performance.

On a Two Dimensional Linear Programming Knapsack Problem with the Extended GUB Constrain (확장된 일반상한제약을 갖는 이차원 선형계획 배낭문제 연구)

  • Won, Joong-Yeon
    • Journal of Korean Institute of Industrial Engineers
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    • v.27 no.1
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    • pp.25-29
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    • 2001
  • We present a two dimensional linear programming knapsack problem with the extended GUB constraint. The presented problem is an extension of the cardinality constrained linear programming knapsack problem. We identify some new properties of the problem and derive a solution algorithm based on the parametric analysis for the knapsack right-hand-side. The solution algorithm has a worst case time complexity of order O($n^2logn$). A numerical example is given.

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The Maximin Linear Programming Knapsack Problem With Extended GUB Constraints (확장된 일반상한제약을 갖는 최대최소 선형계획 배낭문제)

  • 원중연
    • Journal of the Korean Operations Research and Management Science Society
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    • v.26 no.3
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    • pp.95-104
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    • 2001
  • In this paper, we consider a maximin version of the linear programming knapsack problem with extended generalized upper bound (GUB) constraints. We solve the problem efficiently by exploiting its special structure without transforming it into a standard linear programming problem. We present an O(n$^3$) algorithm for deriving the optimal solution where n is the total number of problem variables. We illustrate a numerical example.

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Optimal CNF Encoding for Representing Adjacency in Boolean Cardinality Constraints (이진 기수 조건에서 인접성 표현을 위한 최적화된 CNF 변환)

  • Park, Sa-Choun;Kwon, Gi-Hwon
    • Journal of KIISE:Software and Applications
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    • v.35 no.11
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    • pp.661-670
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    • 2008
  • In some applications of software engineering such as the verification of software model or embedded program, SAT solver is used. To practical use a SAT solver, a problem is encoded to a CNF formula, but because the formula has lower expressiveness than software models or source codes, optimal CNF encoding is required. In this paper, we propose optimal encoding techniques for the problem of "Selecting adjacent $k{\leq}n$ among n objects," Through experimental results we show the proposed constraint is efficient and correct to solve Japanese puzzle. As we know, this paper is the first study about CNF encoding for adjacency in BCC.

Extracting Subsequence of Boolean Variables using SAT-solver (만족가능성 처리기를 이용한 이진 변수 서브시퀀스 추출)

  • Park, Sa-Choun;Kwon, Gi-Hwon
    • The KIPS Transactions:PartD
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    • v.15D no.6
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    • pp.777-784
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    • 2008
  • Recently in the field of model checking, to overcome the state explosion problem, the method of using a SAT-solver is mainly researched. To use a SAT-solver, the system to be verified is translated into CNF and the Boolean cardinality constraint is widely used in translating the system into CNF. In BCC it is dealt with set of boolean variables, but there is no translating method of the sequence among Boolean variables. In this paper, we propose methods for translating the problem, which is extracting a subsequence with length k from a sequence of Boolean variables, into CNF formulas. Through experimental results, we show that our method is more efficient than using only BCC.

Extended GTRBAC Model for Access Control Enforcement in Enterprise Environments (기업환경의 접근제어를 위한 확장된 GTRBAC 모델)

  • Park Dong-Eue;Hwang Yu-Dong
    • Journal of Korea Multimedia Society
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    • v.8 no.2
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    • pp.211-224
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    • 2005
  • With the wide acceptance of the Internet and the Web, volumes of information and related users have increased and companies have become to need security mechanisms to effectively protect important information for business activities and security problems have become increasingly difficult. This paper proposes a improved access control model for access control enforcement in enterprise environments through the integration of the temporal constraint character of the GT-RBAC model and sub-role hierarchies concept. The proposed model, called Extended GT-RBAC(Extended Generalized Temporal Role Based Access Control) Model, supports characteristics of GTRBAC model such as of temporal constraint, various time-constrained cardinality, control now dependency and separation of duty constraints(SoDs). Also it supports unconditional inheritance based on the degree of inheritance and business characteristics by using sub-roles hierarchies in order to allow expressing access control policies at a finer granularity in corporate enterprise environments.

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Extended GTRBAC Delegation Model for Access Control Enforcement in Enterprise Environments (기업환경의 접근제어를 위한 확장된 GTRBAC 위임 모델)

  • Hwang Yu-Dong;Park Dong-Gue
    • Journal of Internet Computing and Services
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    • v.7 no.1
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    • pp.17-30
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    • 2006
  • With the wide acceptance of the Internet and the Web, volumes of information and related users have increased and companies have become to need security mechanisms to effectively protect important information for business activities and security problems have become increasingly difficult. This paper proposes a improved access control model for access control enforcement in enterprise environments through the integration of the temporal constraint character of the GT-RBAC model. sub-role hierarchies concept and PBDM(Permission Based Delegation Model). The proposed model. called Extended GT-RBAC(Extended Generalized Temporal Role Based Access Control) delegation Model. supports characteristics of GTRBAC model such as of temporal constraint, various time-constrained cardinality, control flow dependency and separation of duty constraints (SoDs). Also it supports conditional inheritance based on the degree of inheritance and business characteristics by using sub-roles hierarchies and supports permission based delegation, user to user delegation, role to role delegation, multi-step delegation and temporal delegation by using PBDM.

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