• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.955-962
• /
• 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.

• The Journal of Korean Association of Computer Education
• /
• v.14 no.3
• /
• pp.51-62
• /
• 2011

Navigability refers to how easy a user can find desired information in a web site and is influenced by the structure of a web site. In this paper, we created three types of Web sites, that is a Web site whose structure forms a small world, a Web site whose structure forms a semi-matroid, and a Web site based on an ontology and measured the navigability of each Web site based on two criteria (the number of hyperlinks clicked by users to find the desired information and the elapsed time for finding the desired information). The reason that we selected three structures is because hyperlinks can be created in a way that helps a user find desired information in each site. From the experiments, we found that the average number of hyperlinks which a user clicked to find out the desired information was as follows: a Web site that had semi-matroid property (100.37 hyperlinks) < a Web site that was created based on an ontology (117.63 hyperlinks) < a Web site that had small-world property (236.17 hyperlinks). In addition, we found that the average elapsed time during which a user found out the desired information was as follows: a Web site that was created based on an ontology (20 min 26 sec) < a Web site that had semi-matroid property (23 min 6 sec) < a Web site that had small-world property (30 min 47 sec). Therefore, we can consider a Web site that is created based on a semi-matroid or an ontology is relatively more navigable than a Web site that has small-world property. In this paper, we also propose a way by which our experimental results can be reflected in designing an educational Web site.

• Journal of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.679-684
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.1
• /
• pp.17-25
• /
• 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
• /
• v.51 no.3
• /
• pp.311-322
• /
• 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
• /
• v.5 no.3_4
• /
• pp.255-263
• /
• 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)
• /
• v.9 no.12
• /
• pp.4950-4966
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.169-181
• /
• 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)
• /
• v.14 no.3
• /
• pp.1065-1085
• /
• 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.