• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.431-437
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• 2002

Representing a positive integer in terms of a sum of smaller numbers with certain conditions has been studied since MacMahon [5] pioneered perfect partitions. The complete partitions is in this category and studied by the second author[6]. In this paper, we study complete partitions with more specified completeness, which we call the double-complete partitions.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.267-298
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• 1999

A geometric construction of an exact algebraic formula for graded partition functions, of which a special one is the classical unrestricted partition function p(n), from a diophantine point of view is presented. Moreover, the involved process allows us to compute the value of a graded partition function in an inductive manner with a geometrically built-in self-error-checking ability at each step for correctness of the computed values of the partition function under consideration.

• Bulletin of the Korean Mathematical Society
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• v.59 no.5
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• pp.1279-1287
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• 2022

A partition of n is complete if every positive integer from 1 to n can be represented by the sum of its parts. The concept of complete partitions has been extended in several ways. In this paper, we consider the number of k-relaxed r-complete partitions of n and the number of double-complete partitions of n.

• Journal of Information Processing Systems
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• v.10 no.4
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• pp.568-580
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• 2014

To enhance the utilization of the traffic channels of a network (instead of allocating radio channel to an individual user), a channel or a group of channels are allocated to a user group. The idea behind this is the statistical distribution of traffic arrival rates and the service time for an individual user or a group of users. In this paper, we derive the blocking probability and throughput of a subscriber station of Worldwide Interoperability for Microwave Access (WiMAX) by considering both the connection level and packet-level traffic under a complete partition scheme. The main contribution of the paper is to incorporate the traffic shaping scheme onto the incoming turbulent traffic. Hence, we have also analyzed the impact of the drain rate of the buffer on the blocking probability and throughput.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.22 no.4
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• pp.95-102
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• 2022

This paper proposed a linear time algorithm for a three-partition problem(TPP) in which a polynomial time algorithm is not known as NP-complete. This paper proposes a backtracking method that improves the problems of not being able to obtain a solution of the MM method using the sum of max-min values and third numbers, which are known polynomial algorithms in the past. In addition, the problem of MM applying the backtracking method was improved. The proposed algorithm partition the descending ordered set S into three and assigned to the forward, backward, and best-fit allocation method with maximum margin, and found an optimal solution for 50.00%, which is 5 out of 10 data in initial allocation phase. The remaining five data also showed performance to find the optimal solution by exchanging numbers between surplus boxes and shortage boxes at least once and up to seven times. The proposed algorithm that performs simple allocation and exchange optimization with less O(k) linear time performance complexity than the three-partition m=n/3 data, and it was shown that there could be a polynomial time algorithm in which TPP is a P-problem, not NP-complete.

• Convergence Security Journal
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• v.14 no.7
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• pp.59-64
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• 2014

We investigate $p(n){\cdot}2^{O(\sqrt{n})}$ algorithm for 0/1 knapsack problem where x is the total bit length of a list of sizes of n objects. The algorithm is adaptable of method that achieves a similar complexity for the partition and Subset Sum problem. The method can be applied to other optimization or decision problem based on a list of numerics sizes or weights. 0/1 knapsack problem can be used to solve NP-Complete Problems with pseudo-polynomial time algorithm. We try to apply this technique to bio-informatics problem which has pseudo-polynomial time complexity.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1243-1253
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• 2008

In this paper, we construct one-factorizations of given complete graphs of even order. These constructions partition the edges of the complete graph into one-factors and triples. Our new constructions of one-factors and triples can be applied to a recursive construction of Steiner triple systems for all possible orders ${\geq}$15.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.12B
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• pp.1066-1080
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• 2003

In this paper a scalable QoS routing scheme for distributed multimedia applications in a hierarchical wide area network is proposed. The problem of QoS routing is formulated as a multicriteria shortest path problem, known as NP-complete. The proposed hierarchical routing scheme consists of two phases. In Phase 1, every border node periodically pre-computes the QoS distance for the paths between every pair of border nodes in any level of domain hierarchy. This phase is independet of the QoS request from an application. In Phase II, distributed graph construction algorithm is performed to model the network as a graph by retrieving pre-computed QoS distances. The graph is constructed by the on-demand algorithm and contains a part of the network topology which is completely neglected or partially considered by existing routing schemes, thus maintaining more accurate topology information. By using retrieval approach rather than advertising one, no global QoS state information exchange among nodes is needed. In this Phase, distributed partition algorithm for QoS routing problem is also performed, thus eliminating virtual links on the hierarchically complete path.

• Journal of Electrical Engineering and Technology
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• v.6 no.1
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• pp.48-58
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• 2011

In this paper, an attempt has been made to design the current and speed proportional and integral (PI) regulators of self-commutating current source inverter-fed induction motor drive having capacitors at the machine end and to investigate the transient performance of the same for step changes in reference speed. The mathematical model of the complete drive system is developed in closed loop, and the characteristic equations of the systems are derived using perturbation about steady-state operating point in order to develop the characteristic equations. The D-partition technique is used for finding the stable region in the parametric plane. Frequency scanning technique is used to confirm the stability region. Final selection of the regulator parameters is done by comparing the transient response of the current and speed loops for step variations in reference. The performance of the drive is observed analytically through MATLAB simulation.

• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.685-695
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• 2022

The minimum number of complete bipartite subgraphs needed to partition the edges of a graph G is denoted by b(G). A known lower bound on b(G) states that b(G) ≥ max{p(G), q(G)}, where p(G) and q(G) are the numbers of positive and negative eigenvalues of the adjacency matrix of G, respectively. When equality is attained, G is said to be eigensharp and when b(G) = max{p(G), q(G)} + 1, G is called an almost eigensharp graph. In this paper, we investigate the eigensharpness and almost eigensharpness of lexicographic products of some graphs.