• Proceedings of the Korean Information Science Society Conference
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• 2004.04a
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• pp.952-954
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• 2004

We've developed a Boolean circuit that finds a maximum matching in a convex bipartite graph. This circuit is designed in BC language that was created by K. Park and H. Park(1). The depth of the circuit is O(log$^2$nㆍlog b) and the size is O(bn$^3$). Our circuit gets a triple representation of a convex bipartite graph as its input and produces the maximum matching for its output. We developed some Boolean circuit design techniques that can be used for building other Boolean circuits.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.661-669
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• 2021

For a simple, undirected graph G = (V, E), a perfect Roman dominating function (PRDF) f : V → {0, 1, 2} has the property that, every vertex u with f(u) = 0 is adjacent to exactly one vertex v for which f(v) = 2. The weight of a PRDF is the sum f(V) = ∑_v∈V f(v). The minimum weight of a PRDF is called the perfect Roman domination number, denoted by γ_R^P(G). Given a graph G and a positive integer k, the PRDF problem is to check whether G has a perfect Roman dominating function of weight at most k. In this paper, we first investigate the complexity of PRDF problem for some subclasses of bipartite graphs namely, star convex bipartite graphs and comb convex bipartite graphs. Then we show that PRDF problem is linear time solvable for bounded tree-width graphs, chain graphs and threshold graphs, a subclass of split graphs.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.10a
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• pp.250-278
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• 2004

The product rate variation problem, to be called the PRVP, is to sequence different type units that minimizes the maximum value of a deviation function between ideal and actual rates. The PRVP is an important scheduling problem that arises on mixed-model assembly lines. A surge of research has examined very interesting methods for the PRVP. We believe, however, that several issues are still open with respect to this problem. In this study, we consider convex bipartite graphs, perfect matchings, permanents and balanced sequences. The ultimate objective of this study is to show that we can provide a more efficient and in-depth procedure with a graph theoretic approach in order to solve the PRVP. To achieve this goal, we propose formal alternative proofs for some of the results stated in the previous studies, and establish several new results.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.14 no.4
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• pp.1837-1860
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• 2020

We propose a general framework for studying resource allocation problem and the tradeoff between spectral efficiency (SE) and energy efficiency (EE) for downlink traffic in power domain-non-orthogonal multiple access (PD-NOMA) and device to device (D2D) based heterogeneous cloud radio access networks (H-CRANs) under imperfect channel state information (CSI). The aim is jointly optimize radio remote head (RRH) selection, spectrum allocation and power control, which is formulated as a multi-objective optimization (MOO) problem that can be solved with weighted Tchebycheff method. We propose a low-complexity algorithm to solve user association, spectrum allocation and power coordination separately. We first compute the CSI for RRHs. Then we study allocating the cell users (CUs) and D2D groups to different subchannels by constructing a bipartite graph and Hungrarian algorithm. To solve the power control and EE-SE tradeoff problems, we decompose the target function into two subproblems. Then, we utilize successive convex program approach to lower the computational complexity. Moreover, we use Lagrangian method and KKT conditions to find the global optimum with low complexity, and get a fast convergence by subgradient method. Numerical simulation results demonstrate that by using PD-NOMA technique and H-CRAN with D2D communications, the system gets good EE-SE tradeoff performance.