• 대한수학회보
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• 제52권3호
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• pp.955-962
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• 2015

It has been established that the role played by complete graphs in graph theory is similar to the role Dowling group geometries and Projective geometries play in matroid theory. In this paper, we introduce a notion of H-tree, a class of representable matroids which play a similar role to trees in graph theory. Then we give some properties of H-trees such that when q = 0, then the results reduce to the known properties of trees in graph theory. Finally we give explicit expressions of the characteristic polynomials of H-trees, H-cycles, H-fans and H-wheels.

• 컴퓨터교육학회논문지
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• 제14권3호
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• pp.51-62
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• 2011

항해가능성은 사용자가 웹 사이트에서 원하는 정보를 얼마나 찾기 쉬운지를 말하며 웹 사이트구조에 영향을 받는다. 본 논문에서는 세 종류의 웹 사이트, 즉 작은 세상 구조의 웹 사이트, 준 매트로이드 구조의 웹 사이트, 그리고 온톨로지를 이용한 웹 사이트를 제작하고 각 웹 사이트의 항해 가능성을 두 가지 기준 (사용자가 원하는 정보를 찾기 위해 클릭한 하이퍼링크의 수 및 원하는 정보를 찾기 위해 걸린 시간) 으로 측정하였다. 세가지 구조를 선택한 이유는 각 구조마다 사용자가 정보를 찾기에 도움이 될 수 있도록 하이퍼링크를 만들 수 있기 때문이다. 실험 결과, 한 사용자가 정보를 찾기까지 거쳐 간 링크의 평균 개수는 준 매트로이드 구조의 웹 사이트 (100.37개) < 온톨로지 구조의 웹 사이트 (117.63개) < 작은 세상 구조의 웹 사이트 (236.17개) 순으로 나왔다. 그리고 한 사용자가 정보를 찾는데 소요된 평균 시간은 온톨로지 구조의 웹 사이트 (20분 26초) < 준 매트로이드 구조의 웹 사이트 (23분 6초) < 작은 세상 구조의 웹 사이트(30분 47초) 였다. 따라서 준 매트로이드 구조나 온톨로지 기반 구조의 웹 사이트가 상대적으로 작은 세상 구조의 웹 사이트보다 항해가능 하다고 볼 수 있다. 본 논문에서는 실험 결과를 어떻게 교육용 웹 사이트 설계에 적용할 수 있을 지도 제안하였다.

• 대한수학회지
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• 제33권3호
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• pp.679-684
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• 1996

In this paper we try to investigate the connection between matroids and jump numbers. A couole of papers [3, 5] are known, but they discuss optimization problems with matroid structure. Here we calculate the jump numbers of some bipartite posets which are induced by matroids.

• 대한수학회보
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• 제43권1호
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• pp.17-25
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• 2006

We generalize the results about eigenvalues of random walks on central hyperplane arrangements computed by Bidigare, Hanlon and Rockmore to the cases of random walks on oriented matroids.

• Kyungpook Mathematical Journal
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• 제51권3호
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• pp.311-322
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• 2011

In this paper, we generalize the definition of a closure operator for a finite matroid to a pi-space and obtain the corresponding closure axioms. Then we discuss some properties of pi-spaces using the closure axioms and prove the non-existence for the dual of a pi-space. We also present some results on the automorphism group of a pi-space.

• Journal of Applied and Pure Mathematics
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• 제5권3_4호
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• pp.255-263
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• 2023

In general, the rigidity problem of braced rectangular frameworks is determined by the connectivity of the bipartite graph induced by given rectangular framework. In this paper, we study how to solve the rigidity problem of the braced rectangular framework using the Laplacian matrix of the matrix induced by a braced rectangular framework.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권12호
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• pp.4950-4966
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• 2015

Cloud providers now face the problem of estimating the amount of computing resources required to satisfy a future workload. In this paper, a virtual machine provisioning (VMP) mechanism is designed to adapt workload fluctuation. The arrival rate of forthcoming jobs is predicted for acquiring the proper service rate by adopting an exponential smoothing (ES) method. The proper service rate is estimated to guarantee the service level agreement (SLA) constraints by using a diffusion approximation statistical model. The VMP problem is formulated as a facility location problem. Furthermore, it is characterized as the maximization of submodular function subject to the matroid constraints. A greedy-based VMP algorithm is designed to obtain the optimal virtual machine provision pattern. Simulation results illustrate that the proposed mechanism could increase the average profit efficiently without incurring significant quality of service (QoS) violations.

• 대한수학회지
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• 제56권1호
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• pp.169-181
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• 2019

In [9], Geramita, Harbourne, and Migliore find a graded minimal free resolution of the 2nd order symbolic power of the ideal of a linear star configuration in ${\mathbb{P}}^n$ n of any codimension r. In [8], Geramita, Galetto, Shin, and Van Tuyl extend the result on a general star configuration in ${\mathbb{P}}^n$ but for codimension 2. In this paper, we find a graded minimal free resolution of the 2nd order symbolic power of the ideal of a general star configuration in ${\mathbb{P}}^n$ of any codimension r using a matroid configuration in [10]. This generalizes both the result on a linear star configuration in ${\mathbb{P}}^n$ of codimension r in [9] and the result on a general star configuration in ${\mathbb{P}}^n$ of codimension 2 in [8].

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제14권3호
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• pp.1065-1085
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• 2020

With rapid growth of content demands, device-to-device (D2D) content sharing is exploited to effectively improve the service quality of users. Considering the limited storage space and various content demands of users, caching schemes are significant. However, most of them ignore the influence of the asynchronous content reuse and the selfishness of users. In this work, the user preferences are defined by exploiting the user-oriented content popularity and the current caching situation, and further, we propose the social-aware rate, which comprehensively reflects the achievable contents download rate affected by the social ties, the caching indicators, and the user preferences. Guided by this, we model the collaborative caching problem by making a trade-off between the redundancy of caching contents and the cache hit ratio, with the goal of maximizing the sum of social-aware rate over the constraint of limited storage space. Due to its intractability, it is computationally reduced to the maximization of a monotone submodular function, subject to a matroid constraint. Subsequently, two social-aware collaborative caching algorithms are designed by leveraging the standard and continuous greedy algorithms respectively, which are proved to achieve different approximation ratios in unequal polynomial-time. We present the simulation results to illustrate the performance of our schemes.